Theorem bdayfinbndlem1

Description: Lemma for bdayfinbnd . Show the first half of the inductive step. (Contributed by Scott Fenton, 26-Feb-2026)

	Ref	Expression
Hypotheses	bdayfinbndlem.1	$$⊢\phi \to N\in {\mathbb{N}}_{\mathrm{0s}}$$
	bdayfinbndlem.2	No typesetting found for |- ( ph -> A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
Assertion	bdayfinbndlem1	Could not format assertion : No typesetting found for |- ( ph -> A. w e. No ( ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b

Proof

Step	Hyp	Ref	Expression
1		bdayfinbndlem.1	$$⊢\phi \to N\in {\mathbb{N}}_{\mathrm{0s}}$$
2		bdayfinbndlem.2	Could not format ( ph -> A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
3		bdayn0p1	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to \mathrm{bday}\left(N{+}_s{1}_s\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
4	1 3	syl	$$⊢\phi \to \mathrm{bday}\left(N{+}_s{1}_s\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
5	4	adantr	$$⊢\left(\phi \wedge w\in \mathrm{No}\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
6	5	sseq2d	$$⊢\left(\phi \wedge w\in \mathrm{No}\right)\to \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
7		bdayelon	$$⊢\mathrm{bday}\left(w\right)\in \mathrm{On}$$
8		bdayelon	$$⊢\mathrm{bday}\left(N\right)\in \mathrm{On}$$
9	8	onsuci	$$⊢\mathrm{suc}\mathrm{bday}\left(N\right)\in \mathrm{On}$$
10		onsseleq	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{On}\wedge \mathrm{suc}\mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)\right)$$
11	7 9 10	mp2an	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
12		onsssuc	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
13	7 8 12	mp2an	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
14	13	orbi1i	$$⊢\left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
15	14	bicomi	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
16	11 15	bitri	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
17		fveq2	$$⊢z=w\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(w\right)$$
18	17	sseq1d	$$⊢z=w\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
19		breq2	$$⊢z=w\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}w\right)$$
20	18 19	anbi12d	$$⊢z=w\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}w\right)\right)$$
21		eqeq1	$$⊢z=w\to \left(z=N\leftrightarrow w=N\right)$$
22		eqeq1	Could not format ( z = w -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( z = w -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
23	22	3anbi1d	Could not format ( z = w -> ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
24	23	rexbidv	Could not format ( z = w -> ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
25	24	2rexbidv	Could not format ( z = w -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
26	21 25	orbi12d	Could not format ( z = w -> ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
27	20 26	imbi12d	Could not format ( z = w -> ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
28	27	rspccva	Could not format ( ( A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
29	2 28	sylan	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
30	1	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
31		0n0s	$$⊢0_s\in {\mathbb{N}}_{\mathrm{0s}}$$
32	31	a1i	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to 0_s\in {\mathbb{N}}_{\mathrm{0s}}$$
33		simprr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to w=N$$
34	1	n0snod	$$⊢\phi \to N\in \mathrm{No}$$
35	34	addsridd	$$⊢\phi \to N{+}_s{0}_s=N$$
36	35	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to N{+}_s{0}_s=N$$
37	33 36	eqtr4d	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to w=N{+}_s{0}_s$$
38		0slt1s	$$⊢0_s{<}_s{1}_s$$
39	38	a1i	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to 0_s{<}_s{1}_s$$
40	34	sltp1d	$$⊢\phi \to N{<}_s\left(N{+}_s{1}_s\right)$$
41	35 40	eqbrtrd	$$⊢\phi \to \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)$$
42	41	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)$$
43		oveq1	Could not format ( a = N -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( N +s ( b /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( a = N -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( N +s ( b /su ( 2s ^su q ) ) ) ) with typecode |-
44	43	eqeq2d	Could not format ( a = N -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( N +s ( b /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( a = N -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( N +s ( b /su ( 2s ^su q ) ) ) ) ) with typecode |-
45		oveq1	$$⊢a=N\to a{+}_{s}q=N{+}_{s}q$$
46	45	breq1d	$$⊢a=N\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(N{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
47	44 46	3anbi13d	Could not format ( a = N -> ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s ( b /su ( 2s ^su q ) ) ) /\ b
48		oveq1	Could not format ( b = 0s -> ( b /su ( 2s ^su q ) ) = ( 0s /su ( 2s ^su q ) ) ) : No typesetting found for |- ( b = 0s -> ( b /su ( 2s ^su q ) ) = ( 0s /su ( 2s ^su q ) ) ) with typecode |-
49	48	oveq2d	Could not format ( b = 0s -> ( N +s ( b /su ( 2s ^su q ) ) ) = ( N +s ( 0s /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = 0s -> ( N +s ( b /su ( 2s ^su q ) ) ) = ( N +s ( 0s /su ( 2s ^su q ) ) ) ) with typecode |-
50	49	eqeq2d	Could not format ( b = 0s -> ( w = ( N +s ( b /su ( 2s ^su q ) ) ) <-> w = ( N +s ( 0s /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = 0s -> ( w = ( N +s ( b /su ( 2s ^su q ) ) ) <-> w = ( N +s ( 0s /su ( 2s ^su q ) ) ) ) ) with typecode |-
51		breq1	Could not format ( b = 0s -> ( b 0s ( b 0s
52	50 51	3anbi12d	Could not format ( b = 0s -> ( ( w = ( N +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( ( w = ( N +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s
53		oveq2	Could not format ( q = 0s -> ( 2s ^su q ) = ( 2s ^su 0s ) ) : No typesetting found for |- ( q = 0s -> ( 2s ^su q ) = ( 2s ^su 0s ) ) with typecode |-
54		2sno	Could not format 2s e. No : No typesetting found for |- 2s e. No with typecode |-
55		exps0	Could not format ( 2s e. No -> ( 2s ^su 0s ) = 1s ) : No typesetting found for |- ( 2s e. No -> ( 2s ^su 0s ) = 1s ) with typecode |-
56	54 55	ax-mp	Could not format ( 2s ^su 0s ) = 1s : No typesetting found for |- ( 2s ^su 0s ) = 1s with typecode |-
57	53 56	eqtrdi	Could not format ( q = 0s -> ( 2s ^su q ) = 1s ) : No typesetting found for |- ( q = 0s -> ( 2s ^su q ) = 1s ) with typecode |-
58	57	oveq2d	Could not format ( q = 0s -> ( 0s /su ( 2s ^su q ) ) = ( 0s /su 1s ) ) : No typesetting found for |- ( q = 0s -> ( 0s /su ( 2s ^su q ) ) = ( 0s /su 1s ) ) with typecode |-
59		0sno	$$⊢0_s\in \mathrm{No}$$
60		divs1	$$⊢0_s\in \mathrm{No}\to 0_s{/}_{\mathrm{su}}{1}_s=0_s$$
61	59 60	ax-mp	$$⊢0_s{/}_{\mathrm{su}}{1}_s=0_s$$
62	58 61	eqtrdi	Could not format ( q = 0s -> ( 0s /su ( 2s ^su q ) ) = 0s ) : No typesetting found for |- ( q = 0s -> ( 0s /su ( 2s ^su q ) ) = 0s ) with typecode |-
63	62	oveq2d	Could not format ( q = 0s -> ( N +s ( 0s /su ( 2s ^su q ) ) ) = ( N +s 0s ) ) : No typesetting found for |- ( q = 0s -> ( N +s ( 0s /su ( 2s ^su q ) ) ) = ( N +s 0s ) ) with typecode |-
64	63	eqeq2d	Could not format ( q = 0s -> ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) <-> w = ( N +s 0s ) ) ) : No typesetting found for |- ( q = 0s -> ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) <-> w = ( N +s 0s ) ) ) with typecode |-
65	57	breq2d	Could not format ( q = 0s -> ( 0s 0s ( 0s 0s
66		oveq2	$$⊢q=0_s\to N{+}_{s}q=N{+}_s{0}_s$$
67	66	breq1d	$$⊢q=0_s\to \left(\left(N{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
68	64 65 67	3anbi123d	Could not format ( q = 0s -> ( ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( w = ( N +s 0s ) /\ 0s ( ( w = ( N +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( w = ( N +s 0s ) /\ 0s
69	47 52 68	rspc3ev	Could not format ( ( ( N e. NN0_s /\ 0s e. NN0_s /\ 0s e. NN0_s ) /\ ( w = ( N +s 0s ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
70	30 32 32 37 39 42 69	syl33anc	Could not format ( ( ph /\ ( w e. No /\ w = N ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
71	70	expr	Could not format ( ( ph /\ w e. No ) -> ( w = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
72		idd	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( w = ( x +s ( y /su ( 2s ^su p ) ) ) -> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( w = ( x +s ( y /su ( 2s ^su p ) ) ) -> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
73		idd	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( y y ( y y
74		n0addscl	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in {\mathbb{N}}_{\mathrm{0s}}$$
75	74	n0snod	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in \mathrm{No}$$
76	75	3adant2	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in \mathrm{No}$$
77	76	adantl	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to x{+}_{s}p\in \mathrm{No}$$
78	77	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to x{+}_{s}p\in \mathrm{No}$$
79	34	adantr	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to N\in \mathrm{No}$$
80	79	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N\in \mathrm{No}$$
81		peano2no	$$⊢N\in \mathrm{No}\to N{+}_s{1}_s\in \mathrm{No}$$
82	80 81	syl	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N{+}_s{1}_s\in \mathrm{No}$$
83		simpr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to \left(x{+}_{s}p\right){<}_{s}N$$
84	79	sltp1d	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to N{<}_s\left(N{+}_s{1}_s\right)$$
85	84	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N{<}_s\left(N{+}_s{1}_s\right)$$
86	78 80 82 83 85	slttrd	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)$$
87	86	ex	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to \left(\left(x{+}_{s}p\right){<}_{s}N\to \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
88	72 73 87	3anim123d	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
89		oveq1	Could not format ( a = x -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( x +s ( b /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( a = x -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( x +s ( b /su ( 2s ^su q ) ) ) ) with typecode |-
90	89	eqeq2d	Could not format ( a = x -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( x +s ( b /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( a = x -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( x +s ( b /su ( 2s ^su q ) ) ) ) ) with typecode |-
91		oveq1	$$⊢a=x\to a{+}_{s}q=x{+}_{s}q$$
92	91	breq1d	$$⊢a=x\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(x{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
93	90 92	3anbi13d	Could not format ( a = x -> ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( x +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( x +s ( b /su ( 2s ^su q ) ) ) /\ b
94		oveq1	Could not format ( b = y -> ( b /su ( 2s ^su q ) ) = ( y /su ( 2s ^su q ) ) ) : No typesetting found for |- ( b = y -> ( b /su ( 2s ^su q ) ) = ( y /su ( 2s ^su q ) ) ) with typecode |-
95	94	oveq2d	Could not format ( b = y -> ( x +s ( b /su ( 2s ^su q ) ) ) = ( x +s ( y /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = y -> ( x +s ( b /su ( 2s ^su q ) ) ) = ( x +s ( y /su ( 2s ^su q ) ) ) ) with typecode |-
96	95	eqeq2d	Could not format ( b = y -> ( w = ( x +s ( b /su ( 2s ^su q ) ) ) <-> w = ( x +s ( y /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = y -> ( w = ( x +s ( b /su ( 2s ^su q ) ) ) <-> w = ( x +s ( y /su ( 2s ^su q ) ) ) ) ) with typecode |-
97		breq1	Could not format ( b = y -> ( b y ( b y
98	96 97	3anbi12d	Could not format ( b = y -> ( ( w = ( x +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( x +s ( y /su ( 2s ^su q ) ) ) /\ y ( ( w = ( x +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( x +s ( y /su ( 2s ^su q ) ) ) /\ y
99		oveq2	Could not format ( q = p -> ( 2s ^su q ) = ( 2s ^su p ) ) : No typesetting found for |- ( q = p -> ( 2s ^su q ) = ( 2s ^su p ) ) with typecode |-
100	99	oveq2d	Could not format ( q = p -> ( y /su ( 2s ^su q ) ) = ( y /su ( 2s ^su p ) ) ) : No typesetting found for |- ( q = p -> ( y /su ( 2s ^su q ) ) = ( y /su ( 2s ^su p ) ) ) with typecode |-
101	100	oveq2d	Could not format ( q = p -> ( x +s ( y /su ( 2s ^su q ) ) ) = ( x +s ( y /su ( 2s ^su p ) ) ) ) : No typesetting found for |- ( q = p -> ( x +s ( y /su ( 2s ^su q ) ) ) = ( x +s ( y /su ( 2s ^su p ) ) ) ) with typecode |-
102	101	eqeq2d	Could not format ( q = p -> ( w = ( x +s ( y /su ( 2s ^su q ) ) ) <-> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( q = p -> ( w = ( x +s ( y /su ( 2s ^su q ) ) ) <-> w = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
103	99	breq2d	Could not format ( q = p -> ( y y ( y y
104		oveq2	$$⊢q=p\to x{+}_{s}q=x{+}_{s}p$$
105	104	breq1d	$$⊢q=p\to \left(\left(x{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
106	102 103 105	3anbi123d	Could not format ( q = p -> ( ( w = ( x +s ( y /su ( 2s ^su q ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( w = ( x +s ( y /su ( 2s ^su q ) ) ) /\ y ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
107	93 98 106	rspc3ev	Could not format ( ( ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) /\ ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
108	107	ex	Could not format ( ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) -> ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
109	108	adantl	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
110	88 109	syld	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
111	110	rexlimdvvva	Could not format ( ph -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
112	111	adantr	Could not format ( ( ph /\ w e. No ) -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
113	71 112	jaod	Could not format ( ( ph /\ w e. No ) -> ( ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( w = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
114	29 113	syld	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
115	114	impr	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
116	115	olcd	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) ) ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
117	116	expr	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) C_ ( bday ` N ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
118	117	expd	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) C_ ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) C_ ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
119	5	eqeq2d	$$⊢\left(\phi \wedge w\in \mathrm{No}\right)\to \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
120		df-ne	$$⊢w\ne N{+}_s{1}_s\leftrightarrow \neg w=N{+}_s{1}_s$$
121		simprl	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to w\in \mathrm{No}$$
122		sleloe	$$⊢\left(0_s\in \mathrm{No}\wedge w\in \mathrm{No}\right)\to \left(0_s{\le }_{s}w\leftrightarrow \left(0_s{<}_{s}w\vee 0_s=w\right)\right)$$
123	59 121 122	sylancr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \left(0_s{\le }_{s}w\leftrightarrow \left(0_s{<}_{s}w\vee 0_s=w\right)\right)$$
124		simplrl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to w\in \mathrm{No}$$
125		simpr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to 0_s{<}_{s}w$$
126	124 125	0elleft	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to 0_s\in L\left(w\right)$$
127	126	ne0d	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to L\left(w\right)\ne \varnothing$$
128		simprrl	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
129	128	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
130		peano2n0s	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
131	1 130	syl	$$⊢\phi \to N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
132		n0sbday	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
133	131 132	syl	$$⊢\phi \to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
134	133	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
135	134	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
136	129 135	eqeltrd	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(w\right)\in \mathrm{\omega }$$
137		oldfi	$$⊢\mathrm{bday}\left(w\right)\in \mathrm{\omega }\to \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}$$
138	136 137	syl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}$$
139		leftssold	$$⊢L\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
140		ssfi	$$⊢\left(\mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}\wedge L\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\right)\to L\left(w\right)\in \mathrm{Fin}$$
141	138 139 140	sylancl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to L\left(w\right)\in \mathrm{Fin}$$
142		leftssno	$$⊢L\left(w\right)\subseteq \mathrm{No}$$
143		sltso	$$⊢{<}_s\mathrm{Or}\mathrm{No}$$
144		soss	$$⊢L\left(w\right)\subseteq \mathrm{No}\to \left({<}_s\mathrm{Or}\mathrm{No}\to {<}_s\mathrm{Or}L\left(w\right)\right)$$
145	142 143 144	mp2	$$⊢{<}_s\mathrm{Or}L\left(w\right)$$
146		fimax2g	$$⊢\left({<}_s\mathrm{Or}L\left(w\right)\wedge L\left(w\right)\in \mathrm{Fin}\wedge L\left(w\right)\ne \varnothing \right)\to \exists c\in L\left(w\right)\forall e\in L\left(w\right)\neg c{<}_{s}e$$
147	145 146	mp3an1	$$⊢\left(L\left(w\right)\in \mathrm{Fin}\wedge L\left(w\right)\ne \varnothing \right)\to \exists c\in L\left(w\right)\forall e\in L\left(w\right)\neg c{<}_{s}e$$
148	142	sseli	$$⊢e\in L\left(w\right)\to e\in \mathrm{No}$$
149	142	sseli	$$⊢c\in L\left(w\right)\to c\in \mathrm{No}$$
150		slenlt	$$⊢\left(e\in \mathrm{No}\wedge c\in \mathrm{No}\right)\to \left(e{\le }_{s}c\leftrightarrow \neg c{<}_{s}e\right)$$
151	148 149 150	syl2an	$$⊢\left(e\in L\left(w\right)\wedge c\in L\left(w\right)\right)\to \left(e{\le }_{s}c\leftrightarrow \neg c{<}_{s}e\right)$$
152	151	ancoms	$$⊢\left(c\in L\left(w\right)\wedge e\in L\left(w\right)\right)\to \left(e{\le }_{s}c\leftrightarrow \neg c{<}_{s}e\right)$$
153	152	ralbidva	$$⊢c\in L\left(w\right)\to \left(\forall e\in L\left(w\right)e{\le }_{s}c\leftrightarrow \forall e\in L\left(w\right)\neg c{<}_{s}e\right)$$
154	153	adantl	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge c\in L\left(w\right)\right)\to \left(\forall e\in L\left(w\right)e{\le }_{s}c\leftrightarrow \forall e\in L\left(w\right)\neg c{<}_{s}e\right)$$
155		rightssold	$$⊢R\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
156		ssfi	$$⊢\left(\mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}\wedge R\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\right)\to R\left(w\right)\in \mathrm{Fin}$$
157	138 155 156	sylancl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to R\left(w\right)\in \mathrm{Fin}$$
158	157	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to R\left(w\right)\in \mathrm{Fin}$$
159	124	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to w\in \mathrm{No}$$
160		simprrr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to w\ne N{+}_s{1}_s$$
161	160	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to w\ne N{+}_s{1}_s$$
162	161	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to w\ne N{+}_s{1}_s$$
163	162	neneqd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg w=N{+}_s{1}_s$$
164		simpr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to w\in {On}_s$$
165	131	ad4antr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
166		n0ons	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to N{+}_s{1}_s\in {On}_s$$
167	165 166	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to N{+}_s{1}_s\in {On}_s$$
168	129	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
169	168	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
170		bday11on	$$⊢\left(w\in {On}_s\wedge N{+}_s{1}_s\in {On}_s\wedge \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\right)\to w=N{+}_s{1}_s$$
171	164 167 169 170	syl3anc	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to w=N{+}_s{1}_s$$
172	163 171	mtand	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg w\in {On}_s$$
173		elons	$$⊢w\in {On}_s\leftrightarrow \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
174	173	notbii	$$⊢\neg w\in {On}_s\leftrightarrow \neg \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
175		imnan	$$⊢\left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)\leftrightarrow \neg \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
176	174 175	bitr4i	$$⊢\neg w\in {On}_s\leftrightarrow \left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)$$
177	172 176	sylib	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)$$
178	159 177	mpd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg R\left(w\right)=\varnothing$$
179	178	neqned	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to R\left(w\right)\ne \varnothing$$
180		rightssno	$$⊢R\left(w\right)\subseteq \mathrm{No}$$
181		soss	$$⊢R\left(w\right)\subseteq \mathrm{No}\to \left({<}_s\mathrm{Or}\mathrm{No}\to {<}_s\mathrm{Or}R\left(w\right)\right)$$
182	180 143 181	mp2	$$⊢{<}_s\mathrm{Or}R\left(w\right)$$
183		fimin2g	$$⊢\left({<}_s\mathrm{Or}R\left(w\right)\wedge R\left(w\right)\in \mathrm{Fin}\wedge R\left(w\right)\ne \varnothing \right)\to \exists d\in R\left(w\right)\forall f\in R\left(w\right)\neg f{<}_{s}d$$
184	182 183	mp3an1	$$⊢\left(R\left(w\right)\in \mathrm{Fin}\wedge R\left(w\right)\ne \varnothing \right)\to \exists d\in R\left(w\right)\forall f\in R\left(w\right)\neg f{<}_{s}d$$
185	180	sseli	$$⊢d\in R\left(w\right)\to d\in \mathrm{No}$$
186	180	sseli	$$⊢f\in R\left(w\right)\to f\in \mathrm{No}$$
187		slenlt	$$⊢\left(d\in \mathrm{No}\wedge f\in \mathrm{No}\right)\to \left(d{\le }_{s}f\leftrightarrow \neg f{<}_{s}d\right)$$
188	185 186 187	syl2an	$$⊢\left(d\in R\left(w\right)\wedge f\in R\left(w\right)\right)\to \left(d{\le }_{s}f\leftrightarrow \neg f{<}_{s}d\right)$$
189	188	ralbidva	$$⊢d\in R\left(w\right)\to \left(\forall f\in R\left(w\right)d{\le }_{s}f\leftrightarrow \forall f\in R\left(w\right)\neg f{<}_{s}d\right)$$
190	189	adantl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge d\in R\left(w\right)\right)\to \left(\forall f\in R\left(w\right)d{\le }_{s}f\leftrightarrow \forall f\in R\left(w\right)\neg f{<}_{s}d\right)$$
191		simp2l	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c\in L\left(w\right)$$
192		simp2r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \forall e\in L\left(w\right)e{\le }_{s}c$$
193		simp3l	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to d\in R\left(w\right)$$
194		simp3r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \forall f\in R\left(w\right)d{\le }_{s}f$$
195	191 192 193 194	cutminmax	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to w=\left\{c\right\}{|}_s\left\{d\right\}$$
196		simpl2l	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in L\left(w\right)$$
197	139 196	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
198	142 196	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in \mathrm{No}$$
199		oldbday	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{On}\wedge c\in \mathrm{No}\right)\to \left(c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)\right)$$
200	7 198 199	sylancr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)\right)$$
201	197 200	mpbid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)$$
202	129	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
203	202	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
204	1	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
205	204	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
206	205	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
207	206	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
208	207 3	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
209	203 208	eqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
210	201 209	eleqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
211		bdayelon	$$⊢\mathrm{bday}\left(c\right)\in \mathrm{On}$$
212		onsssuc	$$⊢\left(\mathrm{bday}\left(c\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
213	211 8 212	mp2an	$$⊢\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
214	210 213	sylibr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)$$
215		breq1	$$⊢e=0_s\to \left(e{\le }_{s}c\leftrightarrow 0_s{\le }_{s}c\right)$$
216		simpl2r	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \forall e\in L\left(w\right)e{\le }_{s}c$$
217		simpl1	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)$$
218	217 126	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to 0_s\in L\left(w\right)$$
219	215 216 218	rspcdva	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to 0_s{\le }_{s}c$$
220		fveq2	$$⊢z=c\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(c\right)$$
221	220	sseq1d	$$⊢z=c\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
222		breq2	$$⊢z=c\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}c\right)$$
223	221 222	anbi12d	$$⊢z=c\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}c\right)\right)$$
224		eqeq1	$$⊢z=c\to \left(z=N\leftrightarrow c=N\right)$$
225		eqeq1	Could not format ( z = c -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> c = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( z = c -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> c = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
226	225	3anbi1d	Could not format ( z = c -> ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
227	226	rexbidv	Could not format ( z = c -> ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
228	227	2rexbidv	Could not format ( z = c -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
229		oveq1	Could not format ( x = g -> ( x +s ( y /su ( 2s ^su p ) ) ) = ( g +s ( y /su ( 2s ^su p ) ) ) ) : No typesetting found for |- ( x = g -> ( x +s ( y /su ( 2s ^su p ) ) ) = ( g +s ( y /su ( 2s ^su p ) ) ) ) with typecode |-
230	229	eqeq2d	Could not format ( x = g -> ( c = ( x +s ( y /su ( 2s ^su p ) ) ) <-> c = ( g +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( x = g -> ( c = ( x +s ( y /su ( 2s ^su p ) ) ) <-> c = ( g +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
231		oveq1	$$⊢x=g\to x{+}_{s}p=g{+}_{s}p$$
232	231	breq1d	$$⊢x=g\to \left(\left(x{+}_{s}p\right){<}_{s}N\leftrightarrow \left(g{+}_{s}p\right){<}_{s}N\right)$$
233	230 232	3anbi13d	Could not format ( x = g -> ( ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y
234	233	rexbidv	Could not format ( x = g -> ( E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y
235		oveq1	Could not format ( y = h -> ( y /su ( 2s ^su p ) ) = ( h /su ( 2s ^su p ) ) ) : No typesetting found for |- ( y = h -> ( y /su ( 2s ^su p ) ) = ( h /su ( 2s ^su p ) ) ) with typecode |-
236	235	oveq2d	Could not format ( y = h -> ( g +s ( y /su ( 2s ^su p ) ) ) = ( g +s ( h /su ( 2s ^su p ) ) ) ) : No typesetting found for |- ( y = h -> ( g +s ( y /su ( 2s ^su p ) ) ) = ( g +s ( h /su ( 2s ^su p ) ) ) ) with typecode |-
237	236	eqeq2d	Could not format ( y = h -> ( c = ( g +s ( y /su ( 2s ^su p ) ) ) <-> c = ( g +s ( h /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( y = h -> ( c = ( g +s ( y /su ( 2s ^su p ) ) ) <-> c = ( g +s ( h /su ( 2s ^su p ) ) ) ) ) with typecode |-
238		breq1	Could not format ( y = h -> ( y h ( y h
239	237 238	3anbi12d	Could not format ( y = h -> ( ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h ( ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h
240	239	rexbidv	Could not format ( y = h -> ( E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h ( E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h
241		oveq2	Could not format ( p = i -> ( 2s ^su p ) = ( 2s ^su i ) ) : No typesetting found for |- ( p = i -> ( 2s ^su p ) = ( 2s ^su i ) ) with typecode |-
242	241	oveq2d	Could not format ( p = i -> ( h /su ( 2s ^su p ) ) = ( h /su ( 2s ^su i ) ) ) : No typesetting found for |- ( p = i -> ( h /su ( 2s ^su p ) ) = ( h /su ( 2s ^su i ) ) ) with typecode |-
243	242	oveq2d	Could not format ( p = i -> ( g +s ( h /su ( 2s ^su p ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( p = i -> ( g +s ( h /su ( 2s ^su p ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
244	243	eqeq2d	Could not format ( p = i -> ( c = ( g +s ( h /su ( 2s ^su p ) ) ) <-> c = ( g +s ( h /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( p = i -> ( c = ( g +s ( h /su ( 2s ^su p ) ) ) <-> c = ( g +s ( h /su ( 2s ^su i ) ) ) ) ) with typecode |-
245	241	breq2d	Could not format ( p = i -> ( h h ( h h
246		oveq2	$$⊢p=i\to g{+}_{s}p=g{+}_{s}i$$
247	246	breq1d	$$⊢p=i\to \left(\left(g{+}_{s}p\right){<}_{s}N\leftrightarrow \left(g{+}_{s}i\right){<}_{s}N\right)$$
248	244 245 247	3anbi123d	Could not format ( p = i -> ( ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
249	248	cbvrexvw	Could not format ( E. p e. NN0_s ( c = ( g +s ( h /su ( 2s ^su p ) ) ) /\ h E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
250	240 249	bitrdi	Could not format ( y = h -> ( E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( E. p e. NN0_s ( c = ( g +s ( y /su ( 2s ^su p ) ) ) /\ y E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
251	234 250	cbvrex2vw	Could not format ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( c = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
252	228 251	bitrdi	Could not format ( z = c -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
253	224 252	orbi12d	Could not format ( z = c -> ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
254	223 253	imbi12d	Could not format ( z = c -> ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
255	2	adantr	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) -> A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
256	255	adantr	Could not format ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
257	256	3ad2ant1	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
258	257	adantr	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
259	254 258 198	rspcdva	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
260		simp1ll	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \phi$$
261	260	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \phi$$
262		n0ons	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to N\in {On}_s$$
263	1 262	syl	$$⊢\phi \to N\in {On}_s$$
264	261 263	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in {On}_s$$
265		simpl3l	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in R\left(w\right)$$
266	155 265	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
267		oldbdayim	$$⊢d\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\to \mathrm{bday}\left(d\right)\in \mathrm{bday}\left(w\right)$$
268	266 267	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\in \mathrm{bday}\left(w\right)$$
269	268 209	eleqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
270		bdayelon	$$⊢\mathrm{bday}\left(d\right)\in \mathrm{On}$$
271		onsssuc	$$⊢\left(\mathrm{bday}\left(d\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
272	270 8 271	mp2an	$$⊢\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
273	269 272	sylibr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)$$
274	180 265	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in \mathrm{No}$$
275		madebday	$$⊢\left(\mathrm{bday}\left(N\right)\in \mathrm{On}\wedge d\in \mathrm{No}\right)\to \left(d\in M\left(\mathrm{bday}\left(N\right)\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
276	8 274 275	sylancr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(d\in M\left(\mathrm{bday}\left(N\right)\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
277	273 276	mpbird	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in M\left(\mathrm{bday}\left(N\right)\right)$$
278		onsbnd	$$⊢\left(N\in {On}_s\wedge d\in M\left(\mathrm{bday}\left(N\right)\right)\right)\to d{\le }_{s}N$$
279	264 277 278	syl2anc	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d{\le }_{s}N$$
280	207	n0snod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in \mathrm{No}$$
281	274 280	slenltd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(d{\le }_{s}N\leftrightarrow \neg N{<}_{s}d\right)$$
282	279 281	mpbid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \neg N{<}_{s}d$$
283		lltropt	$$⊢L\left(w\right){\ll }_{s}R\left(w\right)$$
284	283	a1i	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to L\left(w\right){\ll }_{s}R\left(w\right)$$
285	284 191 193	ssltsepcd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c{<}_{s}d$$
286	285	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c{<}_{s}d$$
287		breq1	$$⊢c=N\to \left(c{<}_{s}d\leftrightarrow N{<}_{s}d\right)$$
288	287	bicomd	$$⊢c=N\to \left(N{<}_{s}d\leftrightarrow c{<}_{s}d\right)$$
289	286 288	syl5ibrcom	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(c=N\to N{<}_{s}d\right)$$
290	282 289	mtod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \neg c=N$$
291		orel1	Could not format ( -. c = N -> ( ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
292	290 291	syl	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( c = N \/ E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
293	259 292	syld	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h
294		simp3l1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
295	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
296	295	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
297		simp3l3	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
298	297	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
299		n0addscl	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge i\in {\mathbb{N}}_{\mathrm{0s}}\right)\to g{+}_{s}i\in {\mathbb{N}}_{\mathrm{0s}}$$
300	295 298 299	syl2anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. NN0_s ) with typecode |-
301	300	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. No ) with typecode |-
302	260	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
303	302	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
304	303 34	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
305		n0sge0	$$⊢i\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}i$$
306	298 305	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s i ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s i ) with typecode |-
307	298	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
308	296 307	addsge01d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s i <-> g <_s ( g +s i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s i <-> g <_s ( g +s i ) ) ) with typecode |-
309	306 308	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s ( g +s i ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s ( g +s i ) ) with typecode |-
310		simp3r3	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
311	310	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
312	296 301 304 309 311	slelttrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
313	303 1	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) with typecode |-
314		n0sltp1le	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{<}_{s}N\leftrightarrow \left(g{+}_s{1}_s\right){\le }_{s}N\right)$$
315	295 313 314	syl2anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s N ) ) with typecode |-
316	312 315	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s N ) with typecode |-
317		sltirr	$$⊢N\in \mathrm{No}\to \neg N{<}_{s}N$$
318	304 317	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. N -. N
319		1n0s	$$⊢1_s\in {\mathbb{N}}_{\mathrm{0s}}$$
320		n0addscl	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge 1_s\in {\mathbb{N}}_{\mathrm{0s}}\right)\to g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
321	295 319 320	sylancl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
322	321	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
323	322 304	sltnled	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) -. N <_s ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) -. N <_s ( g +s 1s ) ) ) with typecode |-
324	302	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
325	131	n0snod	$$⊢\phi \to N{+}_s{1}_s\in \mathrm{No}$$
326	324 325	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) with typecode |-
327	324 34	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
328	54	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) with typecode |-
329	327 328	subscld	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 2s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 2s ) e. No ) with typecode |-
330		1sno	$$⊢1_s\in \mathrm{No}$$
331	330	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
332	329 331 331	addsassd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) = ( ( N -s 2s ) +s ( 1s +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) = ( ( N -s 2s ) +s ( 1s +s 1s ) ) ) with typecode |-
333		1p1e2s	Could not format ( 1s +s 1s ) = 2s : No typesetting found for |- ( 1s +s 1s ) = 2s with typecode |-
334	333	oveq2i	Could not format ( ( N -s 2s ) +s ( 1s +s 1s ) ) = ( ( N -s 2s ) +s 2s ) : No typesetting found for |- ( ( N -s 2s ) +s ( 1s +s 1s ) ) = ( ( N -s 2s ) +s 2s ) with typecode |-
335		npcans	Could not format ( ( N e. No /\ 2s e. No ) -> ( ( N -s 2s ) +s 2s ) = N ) : No typesetting found for |- ( ( N e. No /\ 2s e. No ) -> ( ( N -s 2s ) +s 2s ) = N ) with typecode |-
336	327 54 335	sylancl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 2s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 2s ) = N ) with typecode |-
337	334 336	eqtrid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s ( 1s +s 1s ) ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s ( 1s +s 1s ) ) = N ) with typecode |-
338	332 337	eqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) = N ) with typecode |-
339	338 327	eqeltrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 2s ) +s 1s ) +s 1s ) e. No ) with typecode |-
340	329 331	addscld	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. No ) with typecode |-
341	202	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
342	341	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
343		simpl2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
344	142 191	sselid	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c\in \mathrm{No}$$
345	344	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
346	345	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
347	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
348		peano2n0s	$$⊢g\in {\mathbb{N}}_{\mathrm{0s}}\to g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
349	347 348	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
350	349	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
351		subscl	$$⊢\left(N\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to N{-}_s{1}_s\in \mathrm{No}$$
352	34 330 351	sylancl	$$⊢\phi \to N{-}_s{1}_s\in \mathrm{No}$$
353	324 352	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) e. No ) with typecode |-
354		simp3r1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
355	354	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
356		simp3r2	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
357	356	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
358	297	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
359		expscl	Could not format ( ( 2s e. No /\ i e. NN0_s ) -> ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ i e. NN0_s ) -> ( 2s ^su i ) e. No ) with typecode |-
360	54 358 359	sylancr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
361	360	mulslidd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) with typecode |-
362	357 361	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
363		simp3l2	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
364	363	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
365	364	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
366	365 331 358	pw2sltdivmul2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) h ( ( h /su ( 2s ^su i ) ) h
367	362 366	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
368	365 358	pw2divscld	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) with typecode |-
369	347	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
370	368 331 369	sltadd2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) ) ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) )
371	367 370	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) ( g +s ( h /su ( 2s ^su i ) ) )
372	355 371	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
373		n0sltp1le	$$⊢\left(g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(\left(g{+}_s{1}_s\right){<}_{s}N\leftrightarrow \left(\left(g{+}_s{1}_s\right){+}_s{1}_s\right){\le }_{s}N\right)$$
374	321 313 373	syl2anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( ( g +s 1s ) +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( ( g +s 1s ) +s 1s ) <_s N ) ) with typecode |-
375	374	biimpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( ( g +s 1s ) +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( ( g +s 1s ) +s 1s ) <_s N ) ) with typecode |-
376	375	impr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) +s 1s ) <_s N ) with typecode |-
377		npcans	$$⊢\left(N\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(N{-}_s{1}_s\right){+}_s{1}_s=N$$
378	327 330 377	sylancl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 1s ) +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 1s ) +s 1s ) = N ) with typecode |-
379	376 378	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) +s 1s ) <_s ( ( N -s 1s ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) +s 1s ) <_s ( ( N -s 1s ) +s 1s ) ) with typecode |-
380	350 353 331	sleadd1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s ( N -s 1s ) <-> ( ( g +s 1s ) +s 1s ) <_s ( ( N -s 1s ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s ( N -s 1s ) <-> ( ( g +s 1s ) +s 1s ) <_s ( ( N -s 1s ) +s 1s ) ) ) with typecode |-
381	379 380	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s ( N -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s ( N -s 1s ) ) with typecode |-
382	346 350 353 372 381	sltletrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
383	333	oveq2i	Could not format ( N -s ( 1s +s 1s ) ) = ( N -s 2s ) : No typesetting found for |- ( N -s ( 1s +s 1s ) ) = ( N -s 2s ) with typecode |-
384	383	oveq1i	Could not format ( ( N -s ( 1s +s 1s ) ) +s 1s ) = ( ( N -s 2s ) +s 1s ) : No typesetting found for |- ( ( N -s ( 1s +s 1s ) ) +s 1s ) = ( ( N -s 2s ) +s 1s ) with typecode |-
385	327 331 331	subsubs4d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 1s ) -s 1s ) = ( N -s ( 1s +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 1s ) -s 1s ) = ( N -s ( 1s +s 1s ) ) ) with typecode |-
386	385	oveq1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 1s ) -s 1s ) +s 1s ) = ( ( N -s ( 1s +s 1s ) ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 1s ) -s 1s ) +s 1s ) = ( ( N -s ( 1s +s 1s ) ) +s 1s ) ) with typecode |-
387		npcans	$$⊢\left(N{-}_s{1}_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(\left(N{-}_s{1}_s\right){-}_s{1}_s\right){+}_s{1}_s=N{-}_s{1}_s$$
388	353 330 387	sylancl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 1s ) -s 1s ) +s 1s ) = ( N -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( N -s 1s ) -s 1s ) +s 1s ) = ( N -s 1s ) ) with typecode |-
389	386 388	eqtr3d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s ( 1s +s 1s ) ) +s 1s ) = ( N -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s ( 1s +s 1s ) ) +s 1s ) = ( N -s 1s ) ) with typecode |-
390	384 389	eqtr3id	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) = ( N -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) = ( N -s 1s ) ) with typecode |-
391	382 390	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
392	346 340 391	ssltsn	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
393	180 193	sselid	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to d\in \mathrm{No}$$
394	393	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
395	394	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
396		simprl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = N ) with typecode |-
397	396	oveq1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d -s 1s ) = ( N -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d -s 1s ) = ( N -s 1s ) ) with typecode |-
398	397	eqcomd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) = ( d -s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) = ( d -s 1s ) ) with typecode |-
399	395	sltm1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d -s 1s ) ( d -s 1s )
400	398 399	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) ( N -s 1s )
401	390 400	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) ( ( N -s 2s ) +s 1s )
402	340 395 401	ssltsn	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( ( N -s 2s ) +s 1s ) } < { ( ( N -s 2s ) +s 1s ) } <
403	343 340 392 402	ssltbday	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) with typecode |-
404	342 403	eqsstrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) with typecode |-
405	131 166	syl	$$⊢\phi \to N{+}_s{1}_s\in {On}_s$$
406	324 405	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. On_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. On_s ) with typecode |-
407	327 331 328	addsubsd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) -s 2s ) = ( ( N -s 2s ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) -s 2s ) = ( ( N -s 2s ) +s 1s ) ) with typecode |-
408		n0sge0	$$⊢g\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}g$$
409	347 408	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s g ) with typecode |-
410	331 369	addsge01d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s g <-> 1s <_s ( 1s +s g ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s g <-> 1s <_s ( 1s +s g ) ) ) with typecode |-
411	409 410	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( 1s +s g ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( 1s +s g ) ) with typecode |-
412	369 331	addscomd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = ( 1s +s g ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = ( 1s +s g ) ) with typecode |-
413	411 412	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( g +s 1s ) ) with typecode |-
414		simprr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) ( g +s 1s )
415	331 350 327 413 414	slelttrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s 1s
416	331 327 415	sltled	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s N ) with typecode |-
417	331 327 331	sleadd1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s <_s N <-> ( 1s +s 1s ) <_s ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s <_s N <-> ( 1s +s 1s ) <_s ( N +s 1s ) ) ) with typecode |-
418	416 417	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s +s 1s ) <_s ( N +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s +s 1s ) <_s ( N +s 1s ) ) with typecode |-
419	333 418	eqbrtrrid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s <_s ( N +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s <_s ( N +s 1s ) ) with typecode |-
420		2nns	Could not format 2s e. NN_s : No typesetting found for |- 2s e. NN_s with typecode |-
421		nnn0s	Could not format ( 2s e. NN_s -> 2s e. NN0_s ) : No typesetting found for |- ( 2s e. NN_s -> 2s e. NN0_s ) with typecode |-
422	420 421	ax-mp	Could not format 2s e. NN0_s : No typesetting found for |- 2s e. NN0_s with typecode |-
423	422	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. NN0_s ) with typecode |-
424	302 131	syl	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. NN0_s ) with typecode |-
425	424	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. NN0_s ) with typecode |-
426		n0subs	Could not format ( ( 2s e. NN0_s /\ ( N +s 1s ) e. NN0_s ) -> ( 2s <_s ( N +s 1s ) <-> ( ( N +s 1s ) -s 2s ) e. NN0_s ) ) : No typesetting found for |- ( ( 2s e. NN0_s /\ ( N +s 1s ) e. NN0_s ) -> ( 2s <_s ( N +s 1s ) <-> ( ( N +s 1s ) -s 2s ) e. NN0_s ) ) with typecode |-
427	423 425 426	syl2anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s <_s ( N +s 1s ) <-> ( ( N +s 1s ) -s 2s ) e. NN0_s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s <_s ( N +s 1s ) <-> ( ( N +s 1s ) -s 2s ) e. NN0_s ) ) with typecode |-
428	419 427	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) -s 2s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) -s 2s ) e. NN0_s ) with typecode |-
429	407 428	eqeltrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. NN0_s ) with typecode |-
430		n0ons	Could not format ( ( ( N -s 2s ) +s 1s ) e. NN0_s -> ( ( N -s 2s ) +s 1s ) e. On_s ) : No typesetting found for |- ( ( ( N -s 2s ) +s 1s ) e. NN0_s -> ( ( N -s 2s ) +s 1s ) e. On_s ) with typecode |-
431	429 430	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. On_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) e. On_s ) with typecode |-
432	406 431	onsled	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s ( ( N -s 2s ) +s 1s ) <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s ( ( N -s 2s ) +s 1s ) <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` ( ( N -s 2s ) +s 1s ) ) ) ) with typecode |-
433	404 432	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( ( N -s 2s ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( ( N -s 2s ) +s 1s ) ) with typecode |-
434	340	sltp1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N -s 2s ) +s 1s ) ( ( N -s 2s ) +s 1s )
435	326 340 339 433 434	slelttrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) ( N +s 1s )
436	326 339 435	sltled	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( ( ( N -s 2s ) +s 1s ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( ( ( N -s 2s ) +s 1s ) +s 1s ) ) with typecode |-
437	436 338	breqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) with typecode |-
438	324 1	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) with typecode |-
439		n0sltp1le	$$⊢\left(N\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(N{<}_{s}N\leftrightarrow \left(N{+}_s{1}_s\right){\le }_{s}N\right)$$
440	438 438 439	syl2anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N ( N +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N ( N +s 1s ) <_s N ) ) with typecode |-
441	437 440	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
442	441	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) N ( ( g +s 1s ) N
443	323 442	sylbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. N <_s ( g +s 1s ) -> N ( -. N <_s ( g +s 1s ) -> N
444	318 443	mt3d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N <_s ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N <_s ( g +s 1s ) ) with typecode |-
445	444	a1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s N -> N <_s ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s N -> N <_s ( g +s 1s ) ) ) with typecode |-
446	316 445	jcai	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s N /\ N <_s ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s N /\ N <_s ( g +s 1s ) ) ) with typecode |-
447	322 304	sletri3d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) = N <-> ( ( g +s 1s ) <_s N /\ N <_s ( g +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) = N <-> ( ( g +s 1s ) <_s N /\ N <_s ( g +s 1s ) ) ) ) with typecode |-
448	446 447	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) with typecode |-
449	310	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
450		simprr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) with typecode |-
451	449 450	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
452	297	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
453	452	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
454	330	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
455	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
456	455	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
457	453 454 456	sltadd2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i ( g +s i ) ( i ( g +s i )
458	451 457	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i i
459		n0slt1e0	$$⊢i\in {\mathbb{N}}_{\mathrm{0s}}\to \left(i{<}_s{1}_s\leftrightarrow i=0_s\right)$$
460	452 459	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i i = 0s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i i = 0s ) ) with typecode |-
461	458 460	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i = 0s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i = 0s ) with typecode |-
462	354	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
463	356	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
464		oveq2	Could not format ( i = 0s -> ( 2s ^su i ) = ( 2s ^su 0s ) ) : No typesetting found for |- ( i = 0s -> ( 2s ^su i ) = ( 2s ^su 0s ) ) with typecode |-
465	464	adantl	Could not format ( ( ( d = N /\ ( g +s 1s ) = N ) /\ i = 0s ) -> ( 2s ^su i ) = ( 2s ^su 0s ) ) : No typesetting found for |- ( ( ( d = N /\ ( g +s 1s ) = N ) /\ i = 0s ) -> ( 2s ^su i ) = ( 2s ^su 0s ) ) with typecode |-
466	465	adantl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) = ( 2s ^su 0s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) = ( 2s ^su 0s ) ) with typecode |-
467	466 56	eqtrdi	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) = 1s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) = 1s ) with typecode |-
468	463 467	breqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
469	363	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
470		n0slt1e0	$$⊢h\in {\mathbb{N}}_{\mathrm{0s}}\to \left(h{<}_s{1}_s\leftrightarrow h=0_s\right)$$
471	469 470	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h h = 0s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h h = 0s ) ) with typecode |-
472	468 471	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h = 0s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h = 0s ) with typecode |-
473	472 467	oveq12d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( 0s /su 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( 0s /su 1s ) ) with typecode |-
474	473 61	eqtrdi	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = 0s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = 0s ) with typecode |-
475	474	oveq2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) = ( g +s 0s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) = ( g +s 0s ) ) with typecode |-
476	294	n0snod	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
477	476	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
478	477	addsridd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) = g ) with typecode |-
479	462 475 478	3eqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = g ) with typecode |-
480	56	oveq2i	Could not format ( g /su ( 2s ^su 0s ) ) = ( g /su 1s ) : No typesetting found for |- ( g /su ( 2s ^su 0s ) ) = ( g /su 1s ) with typecode |-
481	476	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
482		divs1	$$⊢g\in \mathrm{No}\to g{/}_{\mathrm{su}}{1}_s=g$$
483	481 482	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su 1s ) = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su 1s ) = g ) with typecode |-
484		simprr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = g ) with typecode |-
485	483 484	eqtr4d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su 1s ) = c ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su 1s ) = c ) with typecode |-
486	480 485	eqtrid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = c ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = c ) with typecode |-
487	486	sneqd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g /su ( 2s ^su 0s ) ) } = { c } ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g /su ( 2s ^su 0s ) ) } = { c } ) with typecode |-
488	56	oveq2i	Could not format ( ( g +s 1s ) /su ( 2s ^su 0s ) ) = ( ( g +s 1s ) /su 1s ) : No typesetting found for |- ( ( g +s 1s ) /su ( 2s ^su 0s ) ) = ( ( g +s 1s ) /su 1s ) with typecode |-
489	294 348	syl	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
490	489	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
491	490	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
492		divs1	$$⊢g{+}_s{1}_s\in \mathrm{No}\to \left(g{+}_s{1}_s\right){/}_{\mathrm{su}}{1}_s=g{+}_s{1}_s$$
493	491 492	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su 1s ) = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su 1s ) = ( g +s 1s ) ) with typecode |-
494		simpllr	$$⊢\left(\left(\left(d=N\wedge g{+}_s{1}_s=N\right)\wedge i=0_s\right)\wedge c=g\right)\to g{+}_s{1}_s=N$$
495	494	adantl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) with typecode |-
496		simplll	$$⊢\left(\left(\left(d=N\wedge g{+}_s{1}_s=N\right)\wedge i=0_s\right)\wedge c=g\right)\to d=N$$
497	496	adantl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = N ) with typecode |-
498	495 497	eqtr4d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = d ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = d ) with typecode |-
499	493 498	eqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su 1s ) = d ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su 1s ) = d ) with typecode |-
500	488 499	eqtrid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su ( 2s ^su 0s ) ) = d ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) /su ( 2s ^su 0s ) ) = d ) with typecode |-
501	500	sneqd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } = { d } ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } = { d } ) with typecode |-
502	487 501	oveq12d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) = ( { c } |s { d } ) ) with typecode |-
503	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
504	503	n0zsd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. ZZ_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. ZZ_s ) with typecode |-
505	31	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s e. NN0_s ) with typecode |-
506	504 505	pw2cutp1	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) with typecode |-
507	506	eqcomd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( { ( g /su ( 2s ^su 0s ) ) } |s { ( ( g +s 1s ) /su ( 2s ^su 0s ) ) } ) ) with typecode |-
508		simpl2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
509	502 507 508	3eqtr4rd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) with typecode |-
510		mulscl	Could not format ( ( 2s e. No /\ g e. No ) -> ( 2s x.s g ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ g e. No ) -> ( 2s x.s g ) e. No ) with typecode |-
511	54 481 510	sylancr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s g ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s g ) e. No ) with typecode |-
512	330	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
513		addslid	$$⊢1_s\in \mathrm{No}\to 0_s{+}_s{1}_s=1_s$$
514	330 513	ax-mp	$$⊢0_s{+}_s{1}_s=1_s$$
515	514 319	eqeltri	$$⊢0_s{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
516	515	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s +s 1s ) e. NN0_s ) with typecode |-
517	511 512 516	pw2divsdird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) +s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) +s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) ) ) with typecode |-
518		exps1	Could not format ( 2s e. No -> ( 2s ^su 1s ) = 2s ) : No typesetting found for |- ( 2s e. No -> ( 2s ^su 1s ) = 2s ) with typecode |-
519	54 518	ax-mp	Could not format ( 2s ^su 1s ) = 2s : No typesetting found for |- ( 2s ^su 1s ) = 2s with typecode |-
520	519	oveq1i	Could not format ( ( 2s ^su 1s ) x.s g ) = ( 2s x.s g ) : No typesetting found for |- ( ( 2s ^su 1s ) x.s g ) = ( 2s x.s g ) with typecode |-
521	520	oveq1i	Could not format ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) : No typesetting found for |- ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) with typecode |-
522	319	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. NN0_s ) with typecode |-
523	481 505 522	pw2divscan4d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) ) with typecode |-
524	480 483	eqtrid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g /su ( 2s ^su 0s ) ) = g ) with typecode |-
525	523 524	eqtr3d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su 1s ) x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = g ) with typecode |-
526	521 525	eqtr3id	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) = g ) with typecode |-
527	514	oveq2i	Could not format ( 2s ^su ( 0s +s 1s ) ) = ( 2s ^su 1s ) : No typesetting found for |- ( 2s ^su ( 0s +s 1s ) ) = ( 2s ^su 1s ) with typecode |-
528	527 519	eqtri	Could not format ( 2s ^su ( 0s +s 1s ) ) = 2s : No typesetting found for |- ( 2s ^su ( 0s +s 1s ) ) = 2s with typecode |-
529	528	oveq2i	Could not format ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) = ( 1s /su 2s ) : No typesetting found for |- ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) = ( 1s /su 2s ) with typecode |-
530	529	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) = ( 1s /su 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) = ( 1s /su 2s ) ) with typecode |-
531	526 530	oveq12d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) +s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) ) = ( g +s ( 1s /su 2s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) /su ( 2s ^su ( 0s +s 1s ) ) ) +s ( 1s /su ( 2s ^su ( 0s +s 1s ) ) ) ) = ( g +s ( 1s /su 2s ) ) ) with typecode |-
532	517 531	eqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( g +s ( 1s /su 2s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) = ( g +s ( 1s /su 2s ) ) ) with typecode |-
533	532	eqeq2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) <-> w = ( g +s ( 1s /su 2s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) <-> w = ( g +s ( 1s /su 2s ) ) ) ) with typecode |-
534	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
535	319	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. NN0_s ) with typecode |-
536		simprr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( 1s /su 2s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( 1s /su 2s ) ) ) with typecode |-
537		sltadd1	$$⊢\left(0_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(0_s{<}_s{1}_s\leftrightarrow \left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)\right)$$
538	59 330 330 537	mp3an	$$⊢0_s{<}_s{1}_s\leftrightarrow \left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)$$
539	38 538	mpbi	$$⊢\left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)$$
540	539 514 333	3brtr3i	Could not format 1s
541	540	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s 1s
542		simp-4r	Could not format ( ( ( ( ( d = N /\ ( g +s 1s ) = N ) /\ i = 0s ) /\ c = g ) /\ w = ( g +s ( 1s /su 2s ) ) ) -> ( g +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( d = N /\ ( g +s 1s ) = N ) /\ i = 0s ) /\ c = g ) /\ w = ( g +s ( 1s /su 2s ) ) ) -> ( g +s 1s ) = N ) with typecode |-
543	542	adantl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) = N ) with typecode |-
544	302	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
545	544 34	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
546	545	sltp1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
547	543 546	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) ( g +s 1s )
548		oveq1	Could not format ( a = g -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( b /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( a = g -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( b /su ( 2s ^su q ) ) ) ) with typecode |-
549	548	eqeq2d	Could not format ( a = g -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( b /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( a = g -> ( w = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( b /su ( 2s ^su q ) ) ) ) ) with typecode |-
550		oveq1	$$⊢a=g\to a{+}_{s}q=g{+}_{s}q$$
551	550	breq1d	$$⊢a=g\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
552	549 551	3anbi13d	Could not format ( a = g -> ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b
553		oveq1	Could not format ( b = 1s -> ( b /su ( 2s ^su q ) ) = ( 1s /su ( 2s ^su q ) ) ) : No typesetting found for |- ( b = 1s -> ( b /su ( 2s ^su q ) ) = ( 1s /su ( 2s ^su q ) ) ) with typecode |-
554	553	oveq2d	Could not format ( b = 1s -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( 1s /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = 1s -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( 1s /su ( 2s ^su q ) ) ) ) with typecode |-
555	554	eqeq2d	Could not format ( b = 1s -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( 1s /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = 1s -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( 1s /su ( 2s ^su q ) ) ) ) ) with typecode |-
556		breq1	Could not format ( b = 1s -> ( b 1s ( b 1s
557	555 556	3anbi12d	Could not format ( b = 1s -> ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) /\ 1s ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) /\ 1s
558		oveq2	Could not format ( q = 1s -> ( 2s ^su q ) = ( 2s ^su 1s ) ) : No typesetting found for |- ( q = 1s -> ( 2s ^su q ) = ( 2s ^su 1s ) ) with typecode |-
559	558 519	eqtrdi	Could not format ( q = 1s -> ( 2s ^su q ) = 2s ) : No typesetting found for |- ( q = 1s -> ( 2s ^su q ) = 2s ) with typecode |-
560	559	oveq2d	Could not format ( q = 1s -> ( 1s /su ( 2s ^su q ) ) = ( 1s /su 2s ) ) : No typesetting found for |- ( q = 1s -> ( 1s /su ( 2s ^su q ) ) = ( 1s /su 2s ) ) with typecode |-
561	560	oveq2d	Could not format ( q = 1s -> ( g +s ( 1s /su ( 2s ^su q ) ) ) = ( g +s ( 1s /su 2s ) ) ) : No typesetting found for |- ( q = 1s -> ( g +s ( 1s /su ( 2s ^su q ) ) ) = ( g +s ( 1s /su 2s ) ) ) with typecode |-
562	561	eqeq2d	Could not format ( q = 1s -> ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) <-> w = ( g +s ( 1s /su 2s ) ) ) ) : No typesetting found for |- ( q = 1s -> ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) <-> w = ( g +s ( 1s /su 2s ) ) ) ) with typecode |-
563	559	breq2d	Could not format ( q = 1s -> ( 1s 1s ( 1s 1s
564		oveq2	$$⊢q=1_s\to g{+}_{s}q=g{+}_s{1}_s$$
565	564	breq1d	$$⊢q=1_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s{1}_s\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
566	562 563 565	3anbi123d	Could not format ( q = 1s -> ( ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) /\ 1s ( w = ( g +s ( 1s /su 2s ) ) /\ 1s ( ( w = ( g +s ( 1s /su ( 2s ^su q ) ) ) /\ 1s ( w = ( g +s ( 1s /su 2s ) ) /\ 1s
567	552 557 566	rspc3ev	Could not format ( ( ( g e. NN0_s /\ 1s e. NN0_s /\ 1s e. NN0_s ) /\ ( w = ( g +s ( 1s /su 2s ) ) /\ 1s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
568	534 535 535 536 541 547 567	syl33anc	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
569	568	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( w = ( g +s ( 1s /su 2s ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( 1s /su 2s ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
570	533 569	sylbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( ( ( 2s x.s g ) +s 1s ) /su ( 2s ^su ( 0s +s 1s ) ) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
571	509 570	mpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
572	571	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( c = g -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( c = g -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
573	479 572	mpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
574	573	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i = 0s -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( i = 0s -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
575	461 574	mpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
576	575	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( g +s 1s ) = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
577	448 576	mpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
578	577	ex	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( d = N -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
579		simprr1	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
580		simprr2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
581		simprl3	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
582		expscl	Could not format ( ( 2s e. No /\ l e. NN0_s ) -> ( 2s ^su l ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ l e. NN0_s ) -> ( 2s ^su l ) e. No ) with typecode |-
583	54 581 582	sylancr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. No ) with typecode |-
584	583	mulslidd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su l ) ) = ( 2s ^su l ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su l ) ) = ( 2s ^su l ) ) with typecode |-
585	580 584	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
586		simprl2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) with typecode |-
587	586	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) with typecode |-
588	330	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
589	587 588 581	pw2sltdivmul2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( k /su ( 2s ^su l ) ) k ( ( k /su ( 2s ^su l ) ) k
590	585 589	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) ( k /su ( 2s ^su l ) )
591	587 581	pw2divscld	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) with typecode |-
592		simprl1	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) with typecode |-
593	592	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) with typecode |-
594	591 588 593	sltadd2d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( k /su ( 2s ^su l ) ) ( j +s ( k /su ( 2s ^su l ) ) ) ( ( k /su ( 2s ^su l ) ) ( j +s ( k /su ( 2s ^su l ) ) )
595	590 594	mpbid	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s ( k /su ( 2s ^su l ) ) ) ( j +s ( k /su ( 2s ^su l ) ) )
596	579 595	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d d
597	294	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
598	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
599	598	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
600	599	addsridd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) = g ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) = g ) with typecode |-
601	363	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
602	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
603		n0sge0	$$⊢h\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}h$$
604	602 603	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s h ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s h ) with typecode |-
605	602	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
606	297	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
607	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
608	605 607	pw2ge0divsd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s h <-> 0s <_s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s h <-> 0s <_s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
609	59	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s e. No ) with typecode |-
610	605 607	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) with typecode |-
611	609 610 599	sleadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s ( h /su ( 2s ^su i ) ) <-> ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s ( h /su ( 2s ^su i ) ) <-> ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) ) with typecode |-
612	608 611	bitrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s h <-> ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s h <-> ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) ) with typecode |-
613	604 612	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 0s ) <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
614	600 613	eqbrtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
615	354	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
616	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
617	614 616	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s c ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s c ) with typecode |-
618	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
619	618	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
620	345	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
621	620	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
622	394	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
623	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
624		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s c ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s c ) with typecode |-
625	286	3adant3	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
626	625	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
627	626	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
628	619 621 623 624 627	slelttrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
629	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
630	629	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
631	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
632	592	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) with typecode |-
633		peano2n0s	$$⊢j\in {\mathbb{N}}_{\mathrm{0s}}\to j{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
634	632 633	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s 1s ) e. NN0_s ) with typecode |-
635	634	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s 1s ) e. No ) with typecode |-
636		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
637		simprll	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d d
638	630 631 635 636 637	slttrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
639		n0sleltp1	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge j\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{\le }_{s}j\leftrightarrow g{<}_s\left(j{+}_s{1}_s\right)\right)$$
640	629 632 639	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g <_s j <-> g ( g <_s j <-> g
641	638 640	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s j ) with typecode |-
642	641	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g g <_s j ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g g <_s j ) ) with typecode |-
643	628 642	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g <_s j ) with typecode |-
644	593	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) with typecode |-
645	619 644	sleloed	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g <_s j <-> ( g ( g <_s j <-> ( g
646	592	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) with typecode |-
647		n0sltp1le	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge j\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{<}_{s}j\leftrightarrow \left(g{+}_s{1}_s\right){\le }_{s}j\right)$$
648	618 646 647	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s j ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s j ) ) with typecode |-
649	648	biimpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s j ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g ( g +s 1s ) <_s j ) ) with typecode |-
650	649	impr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) with typecode |-
651	489	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
652	651	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
653	652	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
654	592	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) with typecode |-
655	654	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) with typecode |-
656	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
657		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) with typecode |-
658	586	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) with typecode |-
659		n0sge0	$$⊢k\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}k$$
660	658 659	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s k ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s k ) with typecode |-
661	658	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) with typecode |-
662	581	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
663	661 662	pw2ge0divsd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s k <-> 0s <_s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s k <-> 0s <_s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
664	661 662	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) with typecode |-
665	655 664	addsge01d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s ( k /su ( 2s ^su l ) ) <-> j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s ( k /su ( 2s ^su l ) ) <-> j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) ) with typecode |-
666	663 665	bitrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s k <-> j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s k <-> j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) ) with typecode |-
667	660 666	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
668	579	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
669	667 668	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s d ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s d ) with typecode |-
670	653 655 656 657 669	sletrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s d ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s d ) with typecode |-
671	592	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. NN0_s ) with typecode |-
672	581	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
673		n0addscl	$$⊢\left(j\in {\mathbb{N}}_{\mathrm{0s}}\wedge l\in {\mathbb{N}}_{\mathrm{0s}}\right)\to j{+}_{s}l\in {\mathbb{N}}_{\mathrm{0s}}$$
674	671 672 673	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. NN0_s ) with typecode |-
675	674	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. No ) with typecode |-
676	302	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
677	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
678	677 34	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
679	677 325	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) with typecode |-
680		simprr3	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) ( j +s l )
681	680	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) ( j +s l )
682	678	sltp1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
683	675 678 679 681 682	slttrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) ( j +s l )
684	675 679	sltnled	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( j +s l ) -. ( N +s 1s ) <_s ( j +s l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( j +s l ) -. ( N +s 1s ) <_s ( j +s l ) ) ) with typecode |-
685	683 684	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s ( j +s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s ( j +s l ) ) with typecode |-
686	651	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
687	686	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
688	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
689	687 688	sltnled	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) -. d <_s ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) -. d <_s ( g +s 1s ) ) ) with typecode |-
690	679	adantrr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. No ) with typecode |-
691	593	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j e. No ) with typecode |-
692	675	adantrr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) e. No ) with typecode |-
693	651	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. NN0_s ) with typecode |-
694	693	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. No ) with typecode |-
695	341	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
696	695	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
697		simpll2	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
698	620	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
699	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
700	356	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
701	700	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
702	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
703	54 702 359	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
704	703	mulslidd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) with typecode |-
705	701 704	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
706	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
707	706	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
708	330	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
709	707 708 702	pw2sltdivmul2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) h ( ( h /su ( 2s ^su i ) ) h
710	705 709	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
711	707 702	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) with typecode |-
712	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
713	712	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
714	711 708 713	sltadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) ) ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) )
715	710 714	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) ( g +s ( h /su ( 2s ^su i ) ) )
716	699 715	eqbrtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
717	698 694 716	ssltsn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
718	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
719		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) ( g +s 1s )
720	694 718 719	ssltsn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g +s 1s ) } < { ( g +s 1s ) } <
721	697 694 717 720	ssltbday	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s 1s ) ) ) with typecode |-
722	696 721	eqsstrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s 1s ) ) ) with typecode |-
723	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
724	723 405	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. On_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) e. On_s ) with typecode |-
725		n0ons	$$⊢g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to g{+}_s{1}_s\in {On}_s$$
726	693 725	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. On_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) e. On_s ) with typecode |-
727	724 726	onsled	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s ( g +s 1s ) <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s ( g +s 1s ) <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s 1s ) ) ) ) with typecode |-
728	722 727	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( g +s 1s ) ) with typecode |-
729		simpllr	$$⊢\left(\left(\left(\left(\left(d{<}_s\left(j{+}_s{1}_s\right)\wedge g{\le }_{s}c\right)\wedge g{<}_{s}j\right)\wedge \left(g{+}_s{1}_s\right){\le }_{s}j\right)\wedge \left(g{+}_s{1}_s\right){\le }_{s}d\right)\wedge \left(g{+}_s{1}_s\right){<}_{s}d\right)\to \left(g{+}_s{1}_s\right){\le }_{s}j$$
730	729	adantl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s j ) with typecode |-
731	690 694 691 728 730	sletrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s j ) with typecode |-
732	581	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
733		n0sge0	$$⊢l\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}l$$
734	732 733	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s l ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s l ) with typecode |-
735	732	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) with typecode |-
736	691 735	addsge01d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s l <-> j <_s ( j +s l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 0s <_s l <-> j <_s ( j +s l ) ) ) with typecode |-
737	734 736	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s ( j +s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s j <_s ( j +s l ) ) with typecode |-
738	690 691 692 731 737	sletrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( j +s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s ( j +s l ) ) with typecode |-
739	738	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( N +s 1s ) <_s ( j +s l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) ( N +s 1s ) <_s ( j +s l ) ) ) with typecode |-
740	689 739	sylbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. d <_s ( g +s 1s ) -> ( N +s 1s ) <_s ( j +s l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. d <_s ( g +s 1s ) -> ( N +s 1s ) <_s ( j +s l ) ) ) with typecode |-
741	685 740	mt3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d <_s ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d <_s ( g +s 1s ) ) with typecode |-
742		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s d ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s 1s ) <_s d ) with typecode |-
743	688 687	sletri3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = ( g +s 1s ) <-> ( d <_s ( g +s 1s ) /\ ( g +s 1s ) <_s d ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = ( g +s 1s ) <-> ( d <_s ( g +s 1s ) /\ ( g +s 1s ) <_s d ) ) ) with typecode |-
744	741 742 743	mpbir2and	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) with typecode |-
745	700	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
746	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
747	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
748		n0expscl	Could not format ( ( 2s e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su i ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su i ) e. NN0_s ) with typecode |-
749	422 747 748	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. NN0_s ) with typecode |-
750		n0sltp1le	Could not format ( ( h e. NN0_s /\ ( 2s ^su i ) e. NN0_s ) -> ( h ( h +s 1s ) <_s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( h e. NN0_s /\ ( 2s ^su i ) e. NN0_s ) -> ( h ( h +s 1s ) <_s ( 2s ^su i ) ) ) with typecode |-
751	746 749 750	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h +s 1s ) <_s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h +s 1s ) <_s ( 2s ^su i ) ) ) with typecode |-
752	745 751	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) <_s ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) <_s ( 2s ^su i ) ) with typecode |-
753		peano2n0s	$$⊢h\in {\mathbb{N}}_{\mathrm{0s}}\to h{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
754	363 753	syl	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) with typecode |-
755	754	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) with typecode |-
756	755	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) with typecode |-
757	756	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) with typecode |-
758	749	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
759	757 758	sleloed	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) <_s ( 2s ^su i ) <-> ( ( h +s 1s ) ( ( h +s 1s ) <_s ( 2s ^su i ) <-> ( ( h +s 1s )
760	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
761	34 325	sltnled	$$⊢\phi \to \left(N{<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \neg \left(N{+}_s{1}_s\right){\le }_{s}N\right)$$
762	40 761	mpbid	$$⊢\phi \to \neg \left(N{+}_s{1}_s\right){\le }_{s}N$$
763	760 762	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s N ) with typecode |-
764	695	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
765		simpll2	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
766	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
767	766	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
768	755	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. NN0_s ) with typecode |-
769	768	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) with typecode |-
770	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
771	769 770	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) e. No ) with typecode |-
772	767 771	addscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) e. No ) with typecode |-
773	620	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
774	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
775	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
776	775	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
777	776	sltp1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
778	776 769 770	pw2sltdiv1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h /su ( 2s ^su i ) ) ( h ( h /su ( 2s ^su i ) )
779	777 778	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
780	776 770	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) with typecode |-
781	780 771 767	sltadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) ) ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) )
782	779 781	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) ( g +s ( h /su ( 2s ^su i ) ) )
783	774 782	eqbrtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
784	773 772 783	ssltsn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
785	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
786		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) ( h +s 1s )
787	54 770 359	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
788	787	mulslidd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s x.s ( 2s ^su i ) ) = ( 2s ^su i ) ) with typecode |-
789	786 788	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) ( h +s 1s )
790	330	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
791	769 790 770	pw2sltdivmul2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( h +s 1s ) /su ( 2s ^su i ) ) ( h +s 1s ) ( ( ( h +s 1s ) /su ( 2s ^su i ) ) ( h +s 1s )
792	791	bicomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) ( ( h +s 1s ) /su ( 2s ^su i ) ) ( ( h +s 1s ) ( ( h +s 1s ) /su ( 2s ^su i ) )
793	771 790 767	sltadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( h +s 1s ) /su ( 2s ^su i ) ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ( ( ( h +s 1s ) /su ( 2s ^su i ) ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) )
794	792 793	bitrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ( ( h +s 1s ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) )
795	789 794	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) )
796		simprlr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) with typecode |-
797	795 796	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) )
798	772 785 797	ssltsn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) } < { ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) } <
799	765 772 784 798	ssltbday	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) ) with typecode |-
800	764 799	eqsstrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) ) with typecode |-
801	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
802	801 1	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) with typecode |-
803	310	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
804	803	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
805	802 766 768 770 786 804	bdaypw2bnd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) C_ ( bday ` N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( g +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) C_ ( bday ` N ) ) with typecode |-
806	800 805	sstrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) with typecode |-
807		onslt	$$⊢\left(N\in {On}_s\wedge N{+}_s{1}_s\in {On}_s\right)\to \left(N{<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)\right)$$
808	263 405 807	syl2anc	$$⊢\phi \to \left(N{<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)\right)$$
809	801 808	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) with typecode |-
810	809	notbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. N -. ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. N -. ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) with typecode |-
811	325 34	slenltd	$$⊢\phi \to \left(\left(N{+}_s{1}_s\right){\le }_{s}N\leftrightarrow \neg N{<}_s\left(N{+}_s{1}_s\right)\right)$$
812	801 811	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s N <-> -. N ( ( N +s 1s ) <_s N <-> -. N
813		bdayelon	$$⊢\mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{On}$$
814		ontri1	$$⊢\left(\mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \neg \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)\right)$$
815	813 8 814	mp2an	$$⊢\mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \neg \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)$$
816	815	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) <-> -. ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) <-> -. ( bday ` N ) e. ( bday ` ( N +s 1s ) ) ) ) with typecode |-
817	810 812 816	3bitr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s N <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s N <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) ) with typecode |-
818	806 817	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) with typecode |-
819	818	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) ( N +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) ( N +s 1s ) <_s N ) ) with typecode |-
820	763 819	mtod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( h +s 1s ) -. ( h +s 1s )
821		orel1	Could not format ( -. ( h +s 1s ) ( ( ( h +s 1s ) ( h +s 1s ) = ( 2s ^su i ) ) ) : No typesetting found for |- ( -. ( h +s 1s ) ( ( ( h +s 1s ) ( h +s 1s ) = ( 2s ^su i ) ) ) with typecode |-
822	820 821	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( h +s 1s ) ( h +s 1s ) = ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( h +s 1s ) ( h +s 1s ) = ( 2s ^su i ) ) ) with typecode |-
823	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
824	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
825		n0mulscl	Could not format ( ( 2s e. NN0_s /\ h e. NN0_s ) -> ( 2s x.s h ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ h e. NN0_s ) -> ( 2s x.s h ) e. NN0_s ) with typecode |-
826	422 824 825	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s h ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s h ) e. NN0_s ) with typecode |-
827		n0addscl	Could not format ( ( ( 2s x.s h ) e. NN0_s /\ 1s e. NN0_s ) -> ( ( 2s x.s h ) +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s x.s h ) e. NN0_s /\ 1s e. NN0_s ) -> ( ( 2s x.s h ) +s 1s ) e. NN0_s ) with typecode |-
828	826 319 827	sylancl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) e. NN0_s ) with typecode |-
829		peano2n0s	$$⊢i\in {\mathbb{N}}_{\mathrm{0s}}\to i{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
830	606 829	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s 1s ) e. NN0_s ) with typecode |-
831	830	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s 1s ) e. NN0_s ) with typecode |-
832		simpll2	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
833	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
834	54 606 359	sylancr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
835	834	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
836	823	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
837	835 836	mulscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s g ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s g ) e. No ) with typecode |-
838	601	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
839	838	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
840	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
841	837 839 840	pw2divsdird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
842	836 840	pw2divscan3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) = g ) with typecode |-
843	842	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( h /su ( 2s ^su i ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( h /su ( 2s ^su i ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
844	841 843	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
845	833 844	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) ) with typecode |-
846	845	sneqd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } = { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } = { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } ) with typecode |-
847		simprlr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s 1s ) ) with typecode |-
848	330	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
849	837 839 848	addsassd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) = ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) = ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) ) with typecode |-
850	849	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) ) with typecode |-
851		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) = ( 2s ^su i ) ) with typecode |-
852	851 835	eqeltrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h +s 1s ) e. No ) with typecode |-
853	837 852 840	pw2divsdird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) = ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) ) with typecode |-
854	851	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) = ( ( 2s ^su i ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) = ( ( 2s ^su i ) /su ( 2s ^su i ) ) ) with typecode |-
855	840	pw2divsidd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) /su ( 2s ^su i ) ) = 1s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) /su ( 2s ^su i ) ) = 1s ) with typecode |-
856	854 855	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) = 1s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) /su ( 2s ^su i ) ) = 1s ) with typecode |-
857	842 856	oveq12d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) /su ( 2s ^su i ) ) +s ( ( h +s 1s ) /su ( 2s ^su i ) ) ) = ( g +s 1s ) ) with typecode |-
858	853 857	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su i ) x.s g ) +s ( h +s 1s ) ) /su ( 2s ^su i ) ) = ( g +s 1s ) ) with typecode |-
859	850 858	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) = ( g +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) = ( g +s 1s ) ) with typecode |-
860	847 859	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) ) with typecode |-
861	860	sneqd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { d } = { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { d } = { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) with typecode |-
862	846 861	oveq12d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { c } |s { d } ) = ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { c } |s { d } ) = ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) ) with typecode |-
863	422 840 748	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. NN0_s ) with typecode |-
864		n0mulscl	Could not format ( ( ( 2s ^su i ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su i ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s ^su i ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su i ) x.s g ) e. NN0_s ) with typecode |-
865	863 823 864	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s g ) e. NN0_s ) with typecode |-
866		n0addscl	Could not format ( ( ( ( 2s ^su i ) x.s g ) e. NN0_s /\ h e. NN0_s ) -> ( ( ( 2s ^su i ) x.s g ) +s h ) e. NN0_s ) : No typesetting found for |- ( ( ( ( 2s ^su i ) x.s g ) e. NN0_s /\ h e. NN0_s ) -> ( ( ( 2s ^su i ) x.s g ) +s h ) e. NN0_s ) with typecode |-
867	865 824 866	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) +s h ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) +s h ) e. NN0_s ) with typecode |-
868	867	n0zsd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) +s h ) e. ZZ_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su i ) x.s g ) +s h ) e. ZZ_s ) with typecode |-
869	868 840	pw2cutp1	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) = ( ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) = ( ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
870	54	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) with typecode |-
871	870 837 839	addsdid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) = ( ( 2s x.s ( ( 2s ^su i ) x.s g ) ) +s ( 2s x.s h ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) = ( ( 2s x.s ( ( 2s ^su i ) x.s g ) ) +s ( 2s x.s h ) ) ) with typecode |-
872		expsp1	Could not format ( ( 2s e. No /\ i e. NN0_s ) -> ( 2s ^su ( i +s 1s ) ) = ( ( 2s ^su i ) x.s 2s ) ) : No typesetting found for |- ( ( 2s e. No /\ i e. NN0_s ) -> ( 2s ^su ( i +s 1s ) ) = ( ( 2s ^su i ) x.s 2s ) ) with typecode |-
873	54 840 872	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( ( 2s ^su i ) x.s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( ( 2s ^su i ) x.s 2s ) ) with typecode |-
874	835 870	mulscomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s 2s ) = ( 2s x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s 2s ) = ( 2s x.s ( 2s ^su i ) ) ) with typecode |-
875	873 874	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( 2s x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( 2s x.s ( 2s ^su i ) ) ) with typecode |-
876	875	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i +s 1s ) ) x.s g ) = ( ( 2s x.s ( 2s ^su i ) ) x.s g ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i +s 1s ) ) x.s g ) = ( ( 2s x.s ( 2s ^su i ) ) x.s g ) ) with typecode |-
877	870 835 836	mulsassd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( 2s ^su i ) ) x.s g ) = ( 2s x.s ( ( 2s ^su i ) x.s g ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( 2s ^su i ) ) x.s g ) = ( 2s x.s ( ( 2s ^su i ) x.s g ) ) ) with typecode |-
878	876 877	eqtr2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( 2s ^su i ) x.s g ) ) = ( ( 2s ^su ( i +s 1s ) ) x.s g ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( 2s ^su i ) x.s g ) ) = ( ( 2s ^su ( i +s 1s ) ) x.s g ) ) with typecode |-
879	878	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( 2s ^su i ) x.s g ) ) +s ( 2s x.s h ) ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( 2s ^su i ) x.s g ) ) +s ( 2s x.s h ) ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) ) with typecode |-
880	871 879	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) ) with typecode |-
881	880	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) ) with typecode |-
882	881	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s ( ( ( 2s ^su i ) x.s g ) +s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
883	869 882	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su i ) x.s g ) +s h ) /su ( 2s ^su i ) ) } |s { ( ( ( ( ( 2s ^su i ) x.s g ) +s h ) +s 1s ) /su ( 2s ^su i ) ) } ) = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
884	832 862 883	3eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
885		expscl	Could not format ( ( 2s e. No /\ ( i +s 1s ) e. NN0_s ) -> ( 2s ^su ( i +s 1s ) ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ ( i +s 1s ) e. NN0_s ) -> ( 2s ^su ( i +s 1s ) ) e. No ) with typecode |-
886	54 831 885	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) e. No ) with typecode |-
887	886 836	mulscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i +s 1s ) ) x.s g ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i +s 1s ) ) x.s g ) e. No ) with typecode |-
888	826	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s h ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s h ) e. No ) with typecode |-
889	887 888 848	addsassd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) = ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) ) with typecode |-
890	889	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( 2s x.s h ) ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
891	884 890	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
892	828	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) e. No ) with typecode |-
893	887 892 831	pw2divsdird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) = ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) with typecode |-
894	836 831	pw2divscan3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) = g ) with typecode |-
895	894	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) /su ( 2s ^su ( i +s 1s ) ) ) +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) with typecode |-
896	893 895	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( i +s 1s ) ) x.s g ) +s ( ( 2s x.s h ) +s 1s ) ) /su ( 2s ^su ( i +s 1s ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) with typecode |-
897	891 896	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) with typecode |-
898	848 870 888	sltadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s ( ( 2s x.s h ) +s 1s ) ( 1s ( ( 2s x.s h ) +s 1s )
899	540 898	mpbii	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) ( ( 2s x.s h ) +s 1s )
900	851	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( 2s x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( 2s x.s ( 2s ^su i ) ) ) with typecode |-
901	870 839 848	addsdid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) ) with typecode |-
902		mulsrid	Could not format ( 2s e. No -> ( 2s x.s 1s ) = 2s ) : No typesetting found for |- ( 2s e. No -> ( 2s x.s 1s ) = 2s ) with typecode |-
903	54 902	ax-mp	Could not format ( 2s x.s 1s ) = 2s : No typesetting found for |- ( 2s x.s 1s ) = 2s with typecode |-
904	903	oveq2i	Could not format ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s h ) +s 2s ) : No typesetting found for |- ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s h ) +s 2s ) with typecode |-
905	904	a1i	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) with typecode |-
906	901 905	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( h +s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) with typecode |-
907	900 906	eqtr3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( 2s ^su i ) ) = ( ( 2s x.s h ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( 2s ^su i ) ) = ( ( 2s x.s h ) +s 2s ) ) with typecode |-
908	874 907	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s 2s ) = ( ( 2s x.s h ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su i ) x.s 2s ) = ( ( 2s x.s h ) +s 2s ) ) with typecode |-
909	873 908	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s 1s ) ) = ( ( 2s x.s h ) +s 2s ) ) with typecode |-
910	899 909	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s h ) +s 1s ) ( ( 2s x.s h ) +s 1s )
911	840	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
912	836 911 848	addsassd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s i ) +s 1s ) = ( g +s ( i +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s i ) +s 1s ) = ( g +s ( i +s 1s ) ) ) with typecode |-
913	803	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
914	836 911	addscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) e. No ) with typecode |-
915	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
916	915 34	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
917	914 916 848	sltadd1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s i ) ( ( g +s i ) +s 1s ) ( ( g +s i ) ( ( g +s i ) +s 1s )
918	913 917	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s i ) +s 1s ) ( ( g +s i ) +s 1s )
919	912 918	eqbrtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( i +s 1s ) ) ( g +s ( i +s 1s ) )
920		oveq1	Could not format ( b = ( ( 2s x.s h ) +s 1s ) -> ( b /su ( 2s ^su q ) ) = ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s h ) +s 1s ) -> ( b /su ( 2s ^su q ) ) = ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) with typecode |-
921	920	oveq2d	Could not format ( b = ( ( 2s x.s h ) +s 1s ) -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s h ) +s 1s ) -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) ) with typecode |-
922	921	eqeq2d	Could not format ( b = ( ( 2s x.s h ) +s 1s ) -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s h ) +s 1s ) -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) ) ) with typecode |-
923		breq1	Could not format ( b = ( ( 2s x.s h ) +s 1s ) -> ( b ( ( 2s x.s h ) +s 1s ) ( b ( ( 2s x.s h ) +s 1s )
924	922 923	3anbi12d	Could not format ( b = ( ( 2s x.s h ) +s 1s ) -> ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s h ) +s 1s ) ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s h ) +s 1s )
925		oveq2	Could not format ( q = ( i +s 1s ) -> ( 2s ^su q ) = ( 2s ^su ( i +s 1s ) ) ) : No typesetting found for |- ( q = ( i +s 1s ) -> ( 2s ^su q ) = ( 2s ^su ( i +s 1s ) ) ) with typecode |-
926	925	oveq2d	Could not format ( q = ( i +s 1s ) -> ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) = ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) : No typesetting found for |- ( q = ( i +s 1s ) -> ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) = ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) with typecode |-
927	926	oveq2d	Could not format ( q = ( i +s 1s ) -> ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) : No typesetting found for |- ( q = ( i +s 1s ) -> ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) with typecode |-
928	927	eqeq2d	Could not format ( q = ( i +s 1s ) -> ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) ) : No typesetting found for |- ( q = ( i +s 1s ) -> ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) ) ) with typecode |-
929	925	breq2d	Could not format ( q = ( i +s 1s ) -> ( ( ( 2s x.s h ) +s 1s ) ( ( 2s x.s h ) +s 1s ) ( ( ( 2s x.s h ) +s 1s ) ( ( 2s x.s h ) +s 1s )
930		oveq2	$$⊢q=i{+}_s{1}_s\to g{+}_{s}q=g{+}_s\left(i{+}_s{1}_s\right)$$
931	930	breq1d	$$⊢q=i{+}_s{1}_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s\left(i{+}_s{1}_s\right)\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
932	928 929 931	3anbi123d	Could not format ( q = ( i +s 1s ) -> ( ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s h ) +s 1s ) ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) /\ ( ( 2s x.s h ) +s 1s ) ( ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s h ) +s 1s ) ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) /\ ( ( 2s x.s h ) +s 1s )
933	552 924 932	rspc3ev	Could not format ( ( ( g e. NN0_s /\ ( ( 2s x.s h ) +s 1s ) e. NN0_s /\ ( i +s 1s ) e. NN0_s ) /\ ( w = ( g +s ( ( ( 2s x.s h ) +s 1s ) /su ( 2s ^su ( i +s 1s ) ) ) ) /\ ( ( 2s x.s h ) +s 1s ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
934	823 828 831 897 910 919 933	syl33anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
935	934	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) = ( 2s ^su i ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( h +s 1s ) = ( 2s ^su i ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
936	822 935	syld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( h +s 1s ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( h +s 1s ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
937	759 936	sylbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h +s 1s ) <_s ( 2s ^su i ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( h +s 1s ) <_s ( 2s ^su i ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
938	752 937	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
939	938	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = ( g +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( d = ( g +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
940	939	adantrr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = ( g +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( d = ( g +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
941	744 940	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
942	941	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s d -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( g +s 1s ) <_s d -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
943	670 942	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
944	943	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s 1s ) <_s j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( g +s 1s ) <_s j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
945	650 944	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
946	945	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( g E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
947	626	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
948	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
949	579	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
950		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) with typecode |-
951	950	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( k /su ( 2s ^su l ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( k /su ( 2s ^su l ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
952	949 951	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
953	947 948 952	3brtr3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) ( g +s ( h /su ( 2s ^su i ) ) )
954	838	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
955	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
956	954 955	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) e. No ) with typecode |-
957	587	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) with typecode |-
958	581	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
959	957 958	pw2divscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) e. No ) with typecode |-
960	597	n0snod	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
961	960	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
962	956 959 961	sltadd2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) ) ( ( h /su ( 2s ^su i ) ) ( g +s ( h /su ( 2s ^su i ) ) )
963	953 962	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
964	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
965		simpl3	Could not format ( ( ( j e. NN0_s /\ k e. NN0_s /\ l e. NN0_s ) /\ ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k l e. NN0_s ) : No typesetting found for |- ( ( ( j e. NN0_s /\ k e. NN0_s /\ l e. NN0_s ) /\ ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k l e. NN0_s ) with typecode |-
966	965	adantl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
967	966	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
968	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
969		n0subs	$$⊢\left(l\in {\mathbb{N}}_{\mathrm{0s}}\wedge i\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(l{\le }_{s}i\leftrightarrow i{-}_{s}l\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
970	967 968 969	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i <-> ( i -s l ) e. NN0_s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i <-> ( i -s l ) e. NN0_s ) ) with typecode |-
971	970	biimpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i -> ( i -s l ) e. NN0_s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i -> ( i -s l ) e. NN0_s ) ) with typecode |-
972	971	impr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i -s l ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i -s l ) e. NN0_s ) with typecode |-
973		n0expscl	Could not format ( ( 2s e. NN0_s /\ ( i -s l ) e. NN0_s ) -> ( 2s ^su ( i -s l ) ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ ( i -s l ) e. NN0_s ) -> ( 2s ^su ( i -s l ) ) e. NN0_s ) with typecode |-
974	422 972 973	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i -s l ) ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i -s l ) ) e. NN0_s ) with typecode |-
975	586	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) with typecode |-
976		n0mulscl	Could not format ( ( ( 2s ^su ( i -s l ) ) e. NN0_s /\ k e. NN0_s ) -> ( ( 2s ^su ( i -s l ) ) x.s k ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s ^su ( i -s l ) ) e. NN0_s /\ k e. NN0_s ) -> ( ( 2s ^su ( i -s l ) ) x.s k ) e. NN0_s ) with typecode |-
977	974 975 976	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) e. NN0_s ) with typecode |-
978	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
979		simprlr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
980	966	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
981	980	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) with typecode |-
982	972	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i -s l ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i -s l ) e. No ) with typecode |-
983	981 982	addscomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l +s ( i -s l ) ) = ( ( i -s l ) +s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l +s ( i -s l ) ) = ( ( i -s l ) +s l ) ) with typecode |-
984	978	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
985		npcans	$$⊢\left(i\in \mathrm{No}\wedge l\in \mathrm{No}\right)\to \left(i{-}_{s}l\right){+}_{s}l=i$$
986	984 981 985	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( i -s l ) +s l ) = i ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( i -s l ) +s l ) = i ) with typecode |-
987	983 986	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l +s ( i -s l ) ) = i ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l +s ( i -s l ) ) = i ) with typecode |-
988	987	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l +s ( i -s l ) ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l +s ( i -s l ) ) ) = ( 2s ^su i ) ) with typecode |-
989	988	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) with typecode |-
990	989	eqcomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) ) with typecode |-
991	975	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) with typecode |-
992	991 980 972	pw2divscan4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su ( l +s ( i -s l ) ) ) ) ) with typecode |-
993	990 992	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) = ( k /su ( 2s ^su l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) = ( k /su ( 2s ^su l ) ) ) with typecode |-
994	993	eqcomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k /su ( 2s ^su l ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) with typecode |-
995	979 994	breqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
996	964	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
997	977	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) e. No ) with typecode |-
998	996 997 978	pw2sltdiv1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h /su ( 2s ^su i ) ) ( h ( h /su ( 2s ^su i ) )
999	995 998	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
1000	700	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
1001	580	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
1002		n0expscl	Could not format ( ( 2s e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su l ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su l ) e. NN0_s ) with typecode |-
1003	422 980 1002	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. NN0_s ) with typecode |-
1004	1003	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su l ) e. No ) with typecode |-
1005	974	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i -s l ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i -s l ) ) e. No ) with typecode |-
1006		nnsgt0	Could not format ( 2s e. NN_s -> 0s 0s
1007	420 1006	ax-mp	Could not format 0s
1008		expsgt0	Could not format ( ( 2s e. No /\ ( i -s l ) e. NN0_s /\ 0s 0s 0s
1009	54 1007 1008	mp3an13	Could not format ( ( i -s l ) e. NN0_s -> 0s 0s
1010	972 1009	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
1011	991 1004 1005 1010	sltmul2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( k ( ( 2s ^su ( i -s l ) ) x.s k ) ( k ( ( 2s ^su ( i -s l ) ) x.s k )
1012	1001 1011	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) ( ( 2s ^su ( i -s l ) ) x.s k )
1013		expadds	Could not format ( ( 2s e. No /\ ( i -s l ) e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) : No typesetting found for |- ( ( 2s e. No /\ ( i -s l ) e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) with typecode |-
1014	54 1013	mp3an1	Could not format ( ( ( i -s l ) e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) : No typesetting found for |- ( ( ( i -s l ) e. NN0_s /\ l e. NN0_s ) -> ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) with typecode |-
1015	972 980 1014	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( i -s l ) +s l ) ) = ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) ) with typecode |-
1016	986	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( i -s l ) +s l ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( i -s l ) +s l ) ) = ( 2s ^su i ) ) with typecode |-
1017	1015 1016	eqtr3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) = ( 2s ^su i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s ( 2s ^su l ) ) = ( 2s ^su i ) ) with typecode |-
1018	1012 1017	breqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( i -s l ) ) x.s k ) ( ( 2s ^su ( i -s l ) ) x.s k )
1019	999 1000 1018	3jca	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h
1020	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
1021	579	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1022		simpllr	Could not format ( ( ( ( ( d g = j ) : No typesetting found for |- ( ( ( ( ( d g = j ) with typecode |-
1023	1022	adantl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) with typecode |-
1024	1023 993	oveq12d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1025	1021 1024	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) with typecode |-
1026	803	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s i ) ( g +s i )
1027	1020 1025 1026	3jca	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) /\ ( g +s i ) ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) /\ ( g +s i )
1028		breq1	$$⊢m=h\to \left(m{<}_{s}n\leftrightarrow h{<}_{s}n\right)$$
1029		breq1	Could not format ( m = h -> ( m h ( m h
1030	1028 1029	3anbi12d	Could not format ( m = h -> ( ( m ( h ( ( m ( h
1031		oveq1	Could not format ( m = h -> ( m /su ( 2s ^su o ) ) = ( h /su ( 2s ^su o ) ) ) : No typesetting found for |- ( m = h -> ( m /su ( 2s ^su o ) ) = ( h /su ( 2s ^su o ) ) ) with typecode |-
1032	1031	oveq2d	Could not format ( m = h -> ( g +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( h /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( m = h -> ( g +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( h /su ( 2s ^su o ) ) ) ) with typecode |-
1033	1032	eqeq2d	Could not format ( m = h -> ( c = ( g +s ( m /su ( 2s ^su o ) ) ) <-> c = ( g +s ( h /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( m = h -> ( c = ( g +s ( m /su ( 2s ^su o ) ) ) <-> c = ( g +s ( h /su ( 2s ^su o ) ) ) ) ) with typecode |-
1034	1033	3anbi1d	Could not format ( m = h -> ( ( c = ( g +s ( m /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( ( c = ( g +s ( m /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o )
1035	1030 1034	anbi12d	Could not format ( m = h -> ( ( ( m ( ( h ( ( ( m ( ( h
1036		breq2	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( h h ( h h
1037		breq1	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( n ( ( 2s ^su ( i -s l ) ) x.s k ) ( n ( ( 2s ^su ( i -s l ) ) x.s k )
1038	1036 1037	3anbi13d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( ( h ( h ( ( h ( h
1039		oveq1	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( n /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( n /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) with typecode |-
1040	1039	oveq2d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) ) with typecode |-
1041	1040	eqeq2d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( d = ( g +s ( n /su ( 2s ^su o ) ) ) <-> d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( d = ( g +s ( n /su ( 2s ^su o ) ) ) <-> d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) ) ) with typecode |-
1042	1041	3anbi2d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) /\ ( g +s o )
1043	1038 1042	anbi12d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( ( ( h ( ( h ( ( ( h ( ( h
1044		oveq2	Could not format ( o = i -> ( 2s ^su o ) = ( 2s ^su i ) ) : No typesetting found for |- ( o = i -> ( 2s ^su o ) = ( 2s ^su i ) ) with typecode |-
1045	1044	breq2d	Could not format ( o = i -> ( h h ( h h
1046	1044	breq2d	Could not format ( o = i -> ( ( ( 2s ^su ( i -s l ) ) x.s k ) ( ( 2s ^su ( i -s l ) ) x.s k ) ( ( ( 2s ^su ( i -s l ) ) x.s k ) ( ( 2s ^su ( i -s l ) ) x.s k )
1047	1045 1046	3anbi23d	Could not format ( o = i -> ( ( h ( h ( ( h ( h
1048	1044	oveq2d	Could not format ( o = i -> ( h /su ( 2s ^su o ) ) = ( h /su ( 2s ^su i ) ) ) : No typesetting found for |- ( o = i -> ( h /su ( 2s ^su o ) ) = ( h /su ( 2s ^su i ) ) ) with typecode |-
1049	1048	oveq2d	Could not format ( o = i -> ( g +s ( h /su ( 2s ^su o ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( o = i -> ( g +s ( h /su ( 2s ^su o ) ) ) = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
1050	1049	eqeq2d	Could not format ( o = i -> ( c = ( g +s ( h /su ( 2s ^su o ) ) ) <-> c = ( g +s ( h /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( o = i -> ( c = ( g +s ( h /su ( 2s ^su o ) ) ) <-> c = ( g +s ( h /su ( 2s ^su i ) ) ) ) ) with typecode |-
1051	1044	oveq2d	Could not format ( o = i -> ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) : No typesetting found for |- ( o = i -> ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) with typecode |-
1052	1051	oveq2d	Could not format ( o = i -> ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( o = i -> ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) with typecode |-
1053	1052	eqeq2d	Could not format ( o = i -> ( d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) <-> d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) ) : No typesetting found for |- ( o = i -> ( d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) <-> d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) ) ) with typecode |-
1054		oveq2	$$⊢o=i\to g{+}_{s}o=g{+}_{s}i$$
1055	1054	breq1d	$$⊢o=i\to \left(\left(g{+}_{s}o\right){<}_{s}N\leftrightarrow \left(g{+}_{s}i\right){<}_{s}N\right)$$
1056	1050 1053 1055	3anbi123d	Could not format ( o = i -> ( ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) /\ ( g +s i ) ( ( c = ( g +s ( h /su ( 2s ^su o ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ d = ( g +s ( ( ( 2s ^su ( i -s l ) ) x.s k ) /su ( 2s ^su i ) ) ) /\ ( g +s i )
1057	1047 1056	anbi12d	Could not format ( o = i -> ( ( ( h ( ( h ( ( ( h ( ( h
1058	1035 1043 1057	rspc3ev	Could not format ( ( ( h e. NN0_s /\ ( ( 2s ^su ( i -s l ) ) x.s k ) e. NN0_s /\ i e. NN0_s ) /\ ( ( h E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1059	964 977 978 1019 1027 1058	syl32anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1060	1059	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i -> E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m ( l <_s i -> E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1061		n0subs	$$⊢\left(i\in {\mathbb{N}}_{\mathrm{0s}}\wedge l\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(i{\le }_{s}l\leftrightarrow l{-}_{s}i\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
1062	968 967 1061	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i <_s l <-> ( l -s i ) e. NN0_s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i <_s l <-> ( l -s i ) e. NN0_s ) ) with typecode |-
1063	1062	biimpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i <_s l -> ( l -s i ) e. NN0_s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i <_s l -> ( l -s i ) e. NN0_s ) ) with typecode |-
1064	1063	impr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l -s i ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l -s i ) e. NN0_s ) with typecode |-
1065		n0expscl	Could not format ( ( 2s e. NN0_s /\ ( l -s i ) e. NN0_s ) -> ( 2s ^su ( l -s i ) ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ ( l -s i ) e. NN0_s ) -> ( 2s ^su ( l -s i ) ) e. NN0_s ) with typecode |-
1066	422 1064 1065	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l -s i ) ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l -s i ) ) e. NN0_s ) with typecode |-
1067	601	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. NN0_s ) with typecode |-
1068		n0mulscl	Could not format ( ( ( 2s ^su ( l -s i ) ) e. NN0_s /\ h e. NN0_s ) -> ( ( 2s ^su ( l -s i ) ) x.s h ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s ^su ( l -s i ) ) e. NN0_s /\ h e. NN0_s ) -> ( ( 2s ^su ( l -s i ) ) x.s h ) e. NN0_s ) with typecode |-
1069	1066 1067 1068	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) e. NN0_s ) with typecode |-
1070	586	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. NN0_s ) with typecode |-
1071	966	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. NN0_s ) with typecode |-
1072	1067	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h e. No ) with typecode |-
1073	606	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. NN0_s ) with typecode |-
1074	1072 1073 1064	pw2divscan4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( i +s ( l -s i ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( i +s ( l -s i ) ) ) ) ) with typecode |-
1075	1073	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
1076	1064	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l -s i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l -s i ) e. No ) with typecode |-
1077	1075 1076	addscomd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s ( l -s i ) ) = ( ( l -s i ) +s i ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i +s ( l -s i ) ) = ( ( l -s i ) +s i ) ) with typecode |-
1078	1077	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s ( l -s i ) ) ) = ( 2s ^su ( ( l -s i ) +s i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( i +s ( l -s i ) ) ) = ( 2s ^su ( ( l -s i ) +s i ) ) ) with typecode |-
1079	1078	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( i +s ( l -s i ) ) ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( i +s ( l -s i ) ) ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) ) with typecode |-
1080	1074 1079	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) ) with typecode |-
1081	1071	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) with typecode |-
1082		npcans	$$⊢\left(l\in \mathrm{No}\wedge i\in \mathrm{No}\right)\to \left(l{-}_{s}i\right){+}_{s}i=l$$
1083	1081 1075 1082	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( l -s i ) +s i ) = l ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( l -s i ) +s i ) = l ) with typecode |-
1084	1083	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( l -s i ) +s i ) ) = ( 2s ^su l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( l -s i ) +s i ) ) = ( 2s ^su l ) ) with typecode |-
1085	1084	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su ( ( l -s i ) +s i ) ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) with typecode |-
1086	1080 1085	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) with typecode |-
1087		simprlr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h /su ( 2s ^su i ) ) ( h /su ( 2s ^su i ) )
1088	1086 1087	eqbrtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) )
1089		expscl	Could not format ( ( 2s e. No /\ ( l -s i ) e. NN0_s ) -> ( 2s ^su ( l -s i ) ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ ( l -s i ) e. NN0_s ) -> ( 2s ^su ( l -s i ) ) e. No ) with typecode |-
1090	54 1064 1089	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l -s i ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( l -s i ) ) e. No ) with typecode |-
1091	1090 1072	mulscld	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) e. No ) with typecode |-
1092	1070	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k e. No ) with typecode |-
1093	1091 1092 1071	pw2sltdiv1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) )
1094	1088 1093	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h )
1095	700	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
1096	54 1073 359	sylancr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su i ) e. No ) with typecode |-
1097		expsgt0	Could not format ( ( 2s e. No /\ ( l -s i ) e. NN0_s /\ 0s 0s 0s
1098	54 1007 1097	mp3an13	Could not format ( ( l -s i ) e. NN0_s -> 0s 0s
1099	1064 1098	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
1100	1072 1096 1090 1099	sltmul2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( ( 2s ^su ( l -s i ) ) x.s h ) ( h ( ( 2s ^su ( l -s i ) ) x.s h )
1101	1095 1100	mpbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h )
1102		expadds	Could not format ( ( 2s e. No /\ ( l -s i ) e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( 2s e. No /\ ( l -s i ) e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) with typecode |-
1103	54 1102	mp3an1	Could not format ( ( ( l -s i ) e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( l -s i ) e. NN0_s /\ i e. NN0_s ) -> ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) with typecode |-
1104	1064 1073 1103	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( ( l -s i ) +s i ) ) = ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) ) with typecode |-
1105	1104 1084	eqtr3d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) = ( 2s ^su l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s ( 2s ^su i ) ) = ( 2s ^su l ) ) with typecode |-
1106	1101 1105	breqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h )
1107	580	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
1108	1094 1106 1107	3jca	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h )
1109	615	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( h /su ( 2s ^su i ) ) ) ) with typecode |-
1110	1086	oveq2d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( h /su ( 2s ^su i ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) with typecode |-
1111	1109 1110	eqtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) with typecode |-
1112	579	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1113		simpllr	Could not format ( ( ( ( ( d g = j ) : No typesetting found for |- ( ( ( ( ( d g = j ) with typecode |-
1114	1113	adantl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g = j ) with typecode |-
1115	1114	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( k /su ( 2s ^su l ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( k /su ( 2s ^su l ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1116	1112 1115	eqtr4d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1117	1114	oveq1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s l ) = ( j +s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s l ) = ( j +s l ) ) with typecode |-
1118	680	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) ( j +s l )
1119	1117 1118	eqbrtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s l ) ( g +s l )
1120	1111 1116 1119	3jca	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) /\ d = ( g +s ( k /su ( 2s ^su l ) ) ) /\ ( g +s l ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) /\ d = ( g +s ( k /su ( 2s ^su l ) ) ) /\ ( g +s l )
1121		breq1	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( m ( ( 2s ^su ( l -s i ) ) x.s h ) ( m ( ( 2s ^su ( l -s i ) ) x.s h )
1122		breq1	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( m ( ( 2s ^su ( l -s i ) ) x.s h ) ( m ( ( 2s ^su ( l -s i ) ) x.s h )
1123	1121 1122	3anbi12d	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( ( m ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( m ( ( ( 2s ^su ( l -s i ) ) x.s h )
1124		oveq1	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( m /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( m /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) with typecode |-
1125	1124	oveq2d	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( g +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( g +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) ) with typecode |-
1126	1125	eqeq2d	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( c = ( g +s ( m /su ( 2s ^su o ) ) ) <-> c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( c = ( g +s ( m /su ( 2s ^su o ) ) ) <-> c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) ) ) with typecode |-
1127	1126	3anbi1d	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( ( c = ( g +s ( m /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( ( c = ( g +s ( m /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o )
1128	1123 1127	anbi12d	Could not format ( m = ( ( 2s ^su ( l -s i ) ) x.s h ) -> ( ( ( m ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( m ( ( ( ( 2s ^su ( l -s i ) ) x.s h )
1129		breq2	Could not format ( n = k -> ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h )
1130		breq1	Could not format ( n = k -> ( n k ( n k
1131	1129 1130	3anbi13d	Could not format ( n = k -> ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h )
1132		oveq1	Could not format ( n = k -> ( n /su ( 2s ^su o ) ) = ( k /su ( 2s ^su o ) ) ) : No typesetting found for |- ( n = k -> ( n /su ( 2s ^su o ) ) = ( k /su ( 2s ^su o ) ) ) with typecode |-
1133	1132	oveq2d	Could not format ( n = k -> ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( k /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( n = k -> ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( k /su ( 2s ^su o ) ) ) ) with typecode |-
1134	1133	eqeq2d	Could not format ( n = k -> ( d = ( g +s ( n /su ( 2s ^su o ) ) ) <-> d = ( g +s ( k /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( n = k -> ( d = ( g +s ( n /su ( 2s ^su o ) ) ) <-> d = ( g +s ( k /su ( 2s ^su o ) ) ) ) ) with typecode |-
1135	1134	3anbi2d	Could not format ( n = k -> ( ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( k /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( n /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( k /su ( 2s ^su o ) ) ) /\ ( g +s o )
1136	1131 1135	anbi12d	Could not format ( n = k -> ( ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h )
1137		oveq2	Could not format ( o = l -> ( 2s ^su o ) = ( 2s ^su l ) ) : No typesetting found for |- ( o = l -> ( 2s ^su o ) = ( 2s ^su l ) ) with typecode |-
1138	1137	breq2d	Could not format ( o = l -> ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( 2s ^su ( l -s i ) ) x.s h )
1139	1137	breq2d	Could not format ( o = l -> ( k k ( k k
1140	1138 1139	3anbi23d	Could not format ( o = l -> ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( 2s ^su ( l -s i ) ) x.s h )
1141	1137	oveq2d	Could not format ( o = l -> ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) : No typesetting found for |- ( o = l -> ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) = ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) with typecode |-
1142	1141	oveq2d	Could not format ( o = l -> ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( o = l -> ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) with typecode |-
1143	1142	eqeq2d	Could not format ( o = l -> ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) <-> c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) ) : No typesetting found for |- ( o = l -> ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) <-> c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) ) ) with typecode |-
1144	1137	oveq2d	Could not format ( o = l -> ( k /su ( 2s ^su o ) ) = ( k /su ( 2s ^su l ) ) ) : No typesetting found for |- ( o = l -> ( k /su ( 2s ^su o ) ) = ( k /su ( 2s ^su l ) ) ) with typecode |-
1145	1144	oveq2d	Could not format ( o = l -> ( g +s ( k /su ( 2s ^su o ) ) ) = ( g +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( o = l -> ( g +s ( k /su ( 2s ^su o ) ) ) = ( g +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1146	1145	eqeq2d	Could not format ( o = l -> ( d = ( g +s ( k /su ( 2s ^su o ) ) ) <-> d = ( g +s ( k /su ( 2s ^su l ) ) ) ) ) : No typesetting found for |- ( o = l -> ( d = ( g +s ( k /su ( 2s ^su o ) ) ) <-> d = ( g +s ( k /su ( 2s ^su l ) ) ) ) ) with typecode |-
1147		oveq2	$$⊢o=l\to g{+}_{s}o=g{+}_{s}l$$
1148	1147	breq1d	$$⊢o=l\to \left(\left(g{+}_{s}o\right){<}_{s}N\leftrightarrow \left(g{+}_{s}l\right){<}_{s}N\right)$$
1149	1143 1146 1148	3anbi123d	Could not format ( o = l -> ( ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( k /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) /\ d = ( g +s ( k /su ( 2s ^su l ) ) ) /\ ( g +s l ) ( ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su o ) ) ) /\ d = ( g +s ( k /su ( 2s ^su o ) ) ) /\ ( g +s o ) ( c = ( g +s ( ( ( 2s ^su ( l -s i ) ) x.s h ) /su ( 2s ^su l ) ) ) /\ d = ( g +s ( k /su ( 2s ^su l ) ) ) /\ ( g +s l )
1150	1140 1149	anbi12d	Could not format ( o = l -> ( ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) ( ( ( ( 2s ^su ( l -s i ) ) x.s h )
1151	1128 1136 1150	rspc3ev	Could not format ( ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) e. NN0_s /\ k e. NN0_s /\ l e. NN0_s ) /\ ( ( ( ( 2s ^su ( l -s i ) ) x.s h ) E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1152	1069 1070 1071 1108 1120 1151	syl32anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1153	1152	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( i <_s l -> E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m ( i <_s l -> E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1154	967	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s l e. No ) with typecode |-
1155	968	n0snod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i e. No ) with typecode |-
1156		sletric	$$⊢\left(l\in \mathrm{No}\wedge i\in \mathrm{No}\right)\to \left(l{\le }_{s}i\vee i{\le }_{s}l\right)$$
1157	1154 1155 1156	syl2anc	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i \/ i <_s l ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( l <_s i \/ i <_s l ) ) with typecode |-
1158	1060 1153 1157	mpjaod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m
1159	597	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
1160	1159	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
1161		simprl1	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. NN0_s ) with typecode |-
1162		n0mulscl	Could not format ( ( 2s e. NN0_s /\ m e. NN0_s ) -> ( 2s x.s m ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ m e. NN0_s ) -> ( 2s x.s m ) e. NN0_s ) with typecode |-
1163	422 1161 1162	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s m ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s m ) e. NN0_s ) with typecode |-
1164		peano2n0s	Could not format ( ( 2s x.s m ) e. NN0_s -> ( ( 2s x.s m ) +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( 2s x.s m ) e. NN0_s -> ( ( 2s x.s m ) +s 1s ) e. NN0_s ) with typecode |-
1165	1163 1164	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) e. NN0_s ) with typecode |-
1166		simprl3	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. NN0_s ) with typecode |-
1167		peano2n0s	$$⊢o\in {\mathbb{N}}_{\mathrm{0s}}\to o{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
1168	1166 1167	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( o +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( o +s 1s ) e. NN0_s ) with typecode |-
1169		simpl2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
1170	1169	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
1171	1170	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
1172		simprr1	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m c = ( g +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m c = ( g +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1173	1172	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1174		n0expscl	Could not format ( ( 2s e. NN0_s /\ o e. NN0_s ) -> ( 2s ^su o ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ o e. NN0_s ) -> ( 2s ^su o ) e. NN0_s ) with typecode |-
1175	422 1166 1174	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. NN0_s ) with typecode |-
1176		n0mulscl	Could not format ( ( ( 2s ^su o ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su o ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s ^su o ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su o ) x.s g ) e. NN0_s ) with typecode |-
1177	1175 1160 1176	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s g ) e. NN0_s ) with typecode |-
1178	1177	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s g ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s g ) e. No ) with typecode |-
1179	1161	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. No ) with typecode |-
1180	1178 1179 1166	pw2divsdird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1181	1160	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
1182	1181 1166	pw2divscan3d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) = g ) with typecode |-
1183	1182	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( m /su ( 2s ^su o ) ) ) = ( g +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1184	1180 1183	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) = ( g +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) = ( g +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1185	1173 1184	eqtr4d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) ) with typecode |-
1186	1185	sneqd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } = { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } = { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } ) with typecode |-
1187		simprr2	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m d = ( g +s ( n /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m d = ( g +s ( n /su ( 2s ^su o ) ) ) ) with typecode |-
1188	1187	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( n /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( n /su ( 2s ^su o ) ) ) ) with typecode |-
1189	676	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
1190	1189	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
1191	1190 762	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. ( N +s 1s ) <_s N ) with typecode |-
1192	330	a1i	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s e. No ) with typecode |-
1193		simprl2	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. NN0_s ) with typecode |-
1194	1193	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. No ) with typecode |-
1195	1194 1179	subscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) e. No ) with typecode |-
1196	1192 1195	sltnled	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s -. ( n -s m ) <_s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s -. ( n -s m ) <_s 1s ) ) with typecode |-
1197	695	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
1198	1197	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) = ( bday ` ( N +s 1s ) ) ) with typecode |-
1199	1170	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( { c } |s { d } ) ) with typecode |-
1200	1159	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. NN0_s ) with typecode |-
1201	1200	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g e. No ) with typecode |-
1202	1161	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. NN0_s ) with typecode |-
1203		peano2n0s	$$⊢m\in {\mathbb{N}}_{\mathrm{0s}}\to m{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
1204	1202 1203	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. NN0_s ) with typecode |-
1205	1204	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. No ) with typecode |-
1206	1166	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. NN0_s ) with typecode |-
1207	1205 1206	pw2divscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) /su ( 2s ^su o ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) /su ( 2s ^su o ) ) e. No ) with typecode |-
1208	1201 1207	addscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) e. No ) with typecode |-
1209	620	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
1210	1209	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c e. No ) with typecode |-
1211	1173	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( m /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c = ( g +s ( m /su ( 2s ^su o ) ) ) ) with typecode |-
1212	1179	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m e. No ) with typecode |-
1213	1212	sltp1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1214	1212 1205 1206	pw2sltdiv1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m /su ( 2s ^su o ) ) ( m ( m /su ( 2s ^su o ) )
1215	1212 1206	pw2divscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m /su ( 2s ^su o ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m /su ( 2s ^su o ) ) e. No ) with typecode |-
1216	1215 1207 1201	sltadd2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m /su ( 2s ^su o ) ) ( g +s ( m /su ( 2s ^su o ) ) ) ( ( m /su ( 2s ^su o ) ) ( g +s ( m /su ( 2s ^su o ) ) )
1217	1214 1216	bitrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( g +s ( m /su ( 2s ^su o ) ) ) ( m ( g +s ( m /su ( 2s ^su o ) ) )
1218	1213 1217	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( m /su ( 2s ^su o ) ) ) ( g +s ( m /su ( 2s ^su o ) ) )
1219	1211 1218	eqbrtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
1220	1210 1208 1219	ssltsn	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
1221	622	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
1222	1221	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d e. No ) with typecode |-
1223	1179 1192	addscomd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) = ( 1s +s m ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) = ( 1s +s m ) ) with typecode |-
1224	1223	breq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) ( 1s +s m ) ( ( m +s 1s ) ( 1s +s m )
1225	1192 1179 1194	sltaddsubd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 1s +s m ) 1s ( ( 1s +s m ) 1s
1226	1224 1225	bitrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) 1s ( ( m +s 1s ) 1s
1227	1226	biimprd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s ( m +s 1s ) ( 1s ( m +s 1s )
1228	1227	impr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) ( m +s 1s )
1229	1193	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. NN0_s ) with typecode |-
1230	1229	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n e. No ) with typecode |-
1231	1205 1230 1206	pw2sltdiv1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) ( ( m +s 1s ) /su ( 2s ^su o ) ) ( ( m +s 1s ) ( ( m +s 1s ) /su ( 2s ^su o ) )
1232	1230 1206	pw2divscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n /su ( 2s ^su o ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n /su ( 2s ^su o ) ) e. No ) with typecode |-
1233	1207 1232 1201	sltadd2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( m +s 1s ) /su ( 2s ^su o ) ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ( ( ( m +s 1s ) /su ( 2s ^su o ) ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) )
1234	1231 1233	bitrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ( ( m +s 1s ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) )
1235	1228 1234	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) )
1236	1188	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( n /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( n /su ( 2s ^su o ) ) ) ) with typecode |-
1237	1235 1236	breqtrrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) )
1238	1208 1222 1237	ssltsn	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) } < { ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) } <
1239	1199 1208 1220 1238	ssltbday	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` w ) C_ ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) ) with typecode |-
1240	1198 1239	eqsstrrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) ) with typecode |-
1241	1189	adantr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ph ) with typecode |-
1242	1241 1	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. NN0_s ) with typecode |-
1243		expscl	Could not format ( ( 2s e. No /\ o e. NN0_s ) -> ( 2s ^su o ) e. No ) : No typesetting found for |- ( ( 2s e. No /\ o e. NN0_s ) -> ( 2s ^su o ) e. No ) with typecode |-
1244	54 1166 1243	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. No ) with typecode |-
1245	1244	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su o ) e. No ) with typecode |-
1246		simprl1	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m m m
1247	1246	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1248	1247	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1249		n0sltp1le	$$⊢\left(m\in {\mathbb{N}}_{\mathrm{0s}}\wedge n\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(m{<}_{s}n\leftrightarrow \left(m{+}_s{1}_s\right){\le }_{s}n\right)$$
1250	1202 1229 1249	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s n ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s n ) ) with typecode |-
1251	1248 1250	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) <_s n ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) <_s n ) with typecode |-
1252		simprl3	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m n n
1253	1252	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n n
1254	1253	adantrr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n n
1255	1205 1230 1245 1251 1254	slelttrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) ( m +s 1s )
1256		simprr3	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m ( g +s o ) ( g +s o )
1257	1256	adantr	Could not format ( ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m ( g +s o ) ( g +s o )
1258	1257	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) ( g +s o )
1259	1242 1200 1204 1206 1255 1258	bdaypw2bnd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) C_ ( bday ` N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) C_ ( bday ` N ) ) with typecode |-
1260	1240 1259	sstrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) with typecode |-
1261	405 263	onsled	$$⊢\phi \to \left(\left(N{+}_s{1}_s\right){\le }_{s}N\leftrightarrow \mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
1262	1241 1261	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s N <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( N +s 1s ) <_s N <-> ( bday ` ( N +s 1s ) ) C_ ( bday ` N ) ) ) with typecode |-
1263	1260 1262	mpbird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) <_s N ) with typecode |-
1264	1263	expr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s ( N +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s ( N +s 1s ) <_s N ) ) with typecode |-
1265	1196 1264	sylbird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. ( n -s m ) <_s 1s -> ( N +s 1s ) <_s N ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( -. ( n -s m ) <_s 1s -> ( N +s 1s ) <_s N ) ) with typecode |-
1266	1191 1265	mt3d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) <_s 1s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) <_s 1s ) with typecode |-
1267	1161 1193 1249	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s n ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s n ) ) with typecode |-
1268		npcans	$$⊢\left(n\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(n{-}_s{1}_s\right){+}_s{1}_s=n$$
1269	1194 330 1268	sylancl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s 1s ) +s 1s ) = n ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s 1s ) +s 1s ) = n ) with typecode |-
1270	1269	breq2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) <-> ( m +s 1s ) <_s n ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) <-> ( m +s 1s ) <_s n ) ) with typecode |-
1271	1267 1270	bitr4d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) ) ) with typecode |-
1272	1194 1192	subscld	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s 1s ) e. No ) with typecode |-
1273	1179 1272 1192	sleadd1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m <_s ( n -s 1s ) <-> ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m <_s ( n -s 1s ) <-> ( m +s 1s ) <_s ( ( n -s 1s ) +s 1s ) ) ) with typecode |-
1274	1271 1273	bitr4d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m m <_s ( n -s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m m <_s ( n -s 1s ) ) ) with typecode |-
1275	1179 1194 1192	slesubd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m <_s ( n -s 1s ) <-> 1s <_s ( n -s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m <_s ( n -s 1s ) <-> 1s <_s ( n -s m ) ) ) with typecode |-
1276	1274 1275	bitrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m 1s <_s ( n -s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m 1s <_s ( n -s m ) ) ) with typecode |-
1277	1247 1276	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( n -s m ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s <_s ( n -s m ) ) with typecode |-
1278	1266 1277	jca	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) <_s 1s /\ 1s <_s ( n -s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) <_s 1s /\ 1s <_s ( n -s m ) ) ) with typecode |-
1279	1195 1192	sletri3d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) = 1s <-> ( ( n -s m ) <_s 1s /\ 1s <_s ( n -s m ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) = 1s <-> ( ( n -s m ) <_s 1s /\ 1s <_s ( n -s m ) ) ) ) with typecode |-
1280	1278 1279	mpbird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) = 1s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n -s m ) = 1s ) with typecode |-
1281	1194 1179 1192	subaddsd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) = 1s <-> ( m +s 1s ) = n ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( n -s m ) = 1s <-> ( m +s 1s ) = n ) ) with typecode |-
1282	1280 1281	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) = n ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) = n ) with typecode |-
1283	1282	eqcomd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n = ( m +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n = ( m +s 1s ) ) with typecode |-
1284	1283	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n /su ( 2s ^su o ) ) = ( ( m +s 1s ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( n /su ( 2s ^su o ) ) = ( ( m +s 1s ) /su ( 2s ^su o ) ) ) with typecode |-
1285	1284	oveq2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( n /su ( 2s ^su o ) ) ) = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) with typecode |-
1286	1188 1285	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) with typecode |-
1287	1182	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) with typecode |-
1288	1287	eqcomd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) with typecode |-
1289	1161 1203	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. NN0_s ) with typecode |-
1290	1289	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) e. No ) with typecode |-
1291	1178 1290 1166	pw2divsdird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) /su ( 2s ^su o ) ) +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) ) with typecode |-
1292	1288 1291	eqtr4d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( ( m +s 1s ) /su ( 2s ^su o ) ) ) = ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) ) with typecode |-
1293	1178 1179 1192	addsassd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) = ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) = ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) ) with typecode |-
1294	1293	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) = ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) ) with typecode |-
1295	1294	eqcomd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) = ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su o ) x.s g ) +s ( m +s 1s ) ) /su ( 2s ^su o ) ) = ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) ) with typecode |-
1296	1286 1292 1295	3eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d = ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) ) with typecode |-
1297	1296	sneqd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { d } = { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { d } = { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) with typecode |-
1298	1186 1297	oveq12d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { c } |s { d } ) = ( { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } |s { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { c } |s { d } ) = ( { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } |s { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) ) with typecode |-
1299		n0addscl	Could not format ( ( ( ( 2s ^su o ) x.s g ) e. NN0_s /\ m e. NN0_s ) -> ( ( ( 2s ^su o ) x.s g ) +s m ) e. NN0_s ) : No typesetting found for |- ( ( ( ( 2s ^su o ) x.s g ) e. NN0_s /\ m e. NN0_s ) -> ( ( ( 2s ^su o ) x.s g ) +s m ) e. NN0_s ) with typecode |-
1300	1177 1161 1299	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) +s m ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) +s m ) e. NN0_s ) with typecode |-
1301	1300	n0zsd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) +s m ) e. ZZ_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su o ) x.s g ) +s m ) e. ZZ_s ) with typecode |-
1302	1301 1166	pw2cutp1	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } |s { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) = ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( { ( ( ( ( 2s ^su o ) x.s g ) +s m ) /su ( 2s ^su o ) ) } |s { ( ( ( ( ( 2s ^su o ) x.s g ) +s m ) +s 1s ) /su ( 2s ^su o ) ) } ) = ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) with typecode |-
1303	1171 1298 1302	3eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) with typecode |-
1304	54	a1i	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 2s e. No ) with typecode |-
1305	1304 1178 1179	addsdid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) = ( ( 2s x.s ( ( 2s ^su o ) x.s g ) ) +s ( 2s x.s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) = ( ( 2s x.s ( ( 2s ^su o ) x.s g ) ) +s ( 2s x.s m ) ) ) with typecode |-
1306		expsp1	Could not format ( ( 2s e. No /\ o e. NN0_s ) -> ( 2s ^su ( o +s 1s ) ) = ( ( 2s ^su o ) x.s 2s ) ) : No typesetting found for |- ( ( 2s e. No /\ o e. NN0_s ) -> ( 2s ^su ( o +s 1s ) ) = ( ( 2s ^su o ) x.s 2s ) ) with typecode |-
1307	54 1166 1306	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) = ( ( 2s ^su o ) x.s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) = ( ( 2s ^su o ) x.s 2s ) ) with typecode |-
1308	1244 1304	mulscomd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s 2s ) = ( 2s x.s ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su o ) x.s 2s ) = ( 2s x.s ( 2s ^su o ) ) ) with typecode |-
1309	1307 1308	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) = ( 2s x.s ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) = ( 2s x.s ( 2s ^su o ) ) ) with typecode |-
1310	1309	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) = ( ( 2s x.s ( 2s ^su o ) ) x.s g ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) = ( ( 2s x.s ( 2s ^su o ) ) x.s g ) ) with typecode |-
1311	1304 1244 1181	mulsassd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( 2s ^su o ) ) x.s g ) = ( 2s x.s ( ( 2s ^su o ) x.s g ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( 2s ^su o ) ) x.s g ) = ( 2s x.s ( ( 2s ^su o ) x.s g ) ) ) with typecode |-
1312	1310 1311	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) = ( 2s x.s ( ( 2s ^su o ) x.s g ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) = ( 2s x.s ( ( 2s ^su o ) x.s g ) ) ) with typecode |-
1313	1312	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) = ( ( 2s x.s ( ( 2s ^su o ) x.s g ) ) +s ( 2s x.s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) = ( ( 2s x.s ( ( 2s ^su o ) x.s g ) ) +s ( 2s x.s m ) ) ) with typecode |-
1314	1305 1313	eqtr4d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) ) with typecode |-
1315	1314	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) +s 1s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) +s 1s ) ) with typecode |-
1316		n0expscl	Could not format ( ( 2s e. NN0_s /\ ( o +s 1s ) e. NN0_s ) -> ( 2s ^su ( o +s 1s ) ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ ( o +s 1s ) e. NN0_s ) -> ( 2s ^su ( o +s 1s ) ) e. NN0_s ) with typecode |-
1317	422 1168 1316	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) e. NN0_s ) with typecode |-
1318		n0mulscl	Could not format ( ( ( 2s ^su ( o +s 1s ) ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( 2s ^su ( o +s 1s ) ) e. NN0_s /\ g e. NN0_s ) -> ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. NN0_s ) with typecode |-
1319	1317 1160 1318	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. NN0_s ) with typecode |-
1320	1319	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s ^su ( o +s 1s ) ) x.s g ) e. No ) with typecode |-
1321	1163	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s m ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s m ) e. No ) with typecode |-
1322	1320 1321 1192	addsassd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) +s 1s ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( 2s x.s m ) ) +s 1s ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) ) with typecode |-
1323	1315 1322	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) = ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) ) with typecode |-
1324	1323	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s x.s ( ( ( 2s ^su o ) x.s g ) +s m ) ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) ) with typecode |-
1325	1303 1324	eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) ) with typecode |-
1326	1165	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) e. No ) with typecode |-
1327	1320 1326 1168	pw2divsdird	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) +s ( ( 2s x.s m ) +s 1s ) ) /su ( 2s ^su ( o +s 1s ) ) ) = ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) with typecode |-
1328	1181 1168	pw2divscan3d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) = g ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) = g ) with typecode |-
1329	1328	oveq1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( ( 2s ^su ( o +s 1s ) ) x.s g ) /su ( 2s ^su ( o +s 1s ) ) ) +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) with typecode |-
1330	1325 1327 1329	3eqtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) with typecode |-
1331		n0mulscl	Could not format ( ( 2s e. NN0_s /\ ( m +s 1s ) e. NN0_s ) -> ( 2s x.s ( m +s 1s ) ) e. NN0_s ) : No typesetting found for |- ( ( 2s e. NN0_s /\ ( m +s 1s ) e. NN0_s ) -> ( 2s x.s ( m +s 1s ) ) e. NN0_s ) with typecode |-
1332	422 1289 1331	sylancr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) e. NN0_s ) with typecode |-
1333	1332	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) e. No ) with typecode |-
1334	1317	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s ^su ( o +s 1s ) ) e. No ) with typecode |-
1335	1192 1304 1321	sltadd2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 1s ( ( 2s x.s m ) +s 1s ) ( 1s ( ( 2s x.s m ) +s 1s )
1336	540 1335	mpbii	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) ( ( 2s x.s m ) +s 1s )
1337	1304 1179 1192	addsdid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) = ( ( 2s x.s m ) +s ( 2s x.s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) = ( ( 2s x.s m ) +s ( 2s x.s 1s ) ) ) with typecode |-
1338	903	oveq2i	Could not format ( ( 2s x.s m ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s m ) +s 2s ) : No typesetting found for |- ( ( 2s x.s m ) +s ( 2s x.s 1s ) ) = ( ( 2s x.s m ) +s 2s ) with typecode |-
1339	1337 1338	eqtrdi	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) = ( ( 2s x.s m ) +s 2s ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) = ( ( 2s x.s m ) +s 2s ) ) with typecode |-
1340	1336 1339	breqtrrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) ( ( 2s x.s m ) +s 1s )
1341		simprl2	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m m m
1342	1341	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1343		n0sltp1le	Could not format ( ( m e. NN0_s /\ ( 2s ^su o ) e. NN0_s ) -> ( m ( m +s 1s ) <_s ( 2s ^su o ) ) ) : No typesetting found for |- ( ( m e. NN0_s /\ ( 2s ^su o ) e. NN0_s ) -> ( m ( m +s 1s ) <_s ( 2s ^su o ) ) ) with typecode |-
1344	1161 1175 1343	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m ( m +s 1s ) <_s ( 2s ^su o ) ) ) with typecode |-
1345	1342 1344	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) <_s ( 2s ^su o ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) <_s ( 2s ^su o ) ) with typecode |-
1346	1007	a1i	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
1347	1290 1244 1304 1346	slemul2d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) <_s ( 2s ^su o ) <-> ( 2s x.s ( m +s 1s ) ) <_s ( 2s x.s ( 2s ^su o ) ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( m +s 1s ) <_s ( 2s ^su o ) <-> ( 2s x.s ( m +s 1s ) ) <_s ( 2s x.s ( 2s ^su o ) ) ) ) with typecode |-
1348	1345 1347	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) <_s ( 2s x.s ( 2s ^su o ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) <_s ( 2s x.s ( 2s ^su o ) ) ) with typecode |-
1349	1348 1309	breqtrrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) <_s ( 2s ^su ( o +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( 2s x.s ( m +s 1s ) ) <_s ( 2s ^su ( o +s 1s ) ) ) with typecode |-
1350	1326 1333 1334 1340 1349	sltletrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( 2s x.s m ) +s 1s ) ( ( 2s x.s m ) +s 1s )
1351	1166	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s o e. No ) with typecode |-
1352	1181 1351 1192	addsassd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s o ) +s 1s ) = ( g +s ( o +s 1s ) ) ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s o ) +s 1s ) = ( g +s ( o +s 1s ) ) ) with typecode |-
1353	1256	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) ( g +s o )
1354		n0addscl	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge o\in {\mathbb{N}}_{\mathrm{0s}}\right)\to g{+}_{s}o\in {\mathbb{N}}_{\mathrm{0s}}$$
1355	1160 1166 1354	syl2anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) e. NN0_s ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) e. NN0_s ) with typecode |-
1356	1355	n0snod	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) e. No ) with typecode |-
1357	1190 34	syl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) : No typesetting found for |- ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N e. No ) with typecode |-
1358	1356 1357 1192	sltadd1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s o ) ( ( g +s o ) +s 1s ) ( ( g +s o ) ( ( g +s o ) +s 1s )
1359	1353 1358	mpbid	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g +s o ) +s 1s ) ( ( g +s o ) +s 1s )
1360	1352 1359	eqbrtrrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s ( o +s 1s ) ) ( g +s ( o +s 1s ) )
1361		oveq1	Could not format ( b = ( ( 2s x.s m ) +s 1s ) -> ( b /su ( 2s ^su q ) ) = ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s m ) +s 1s ) -> ( b /su ( 2s ^su q ) ) = ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) with typecode |-
1362	1361	oveq2d	Could not format ( b = ( ( 2s x.s m ) +s 1s ) -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s m ) +s 1s ) -> ( g +s ( b /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) ) with typecode |-
1363	1362	eqeq2d	Could not format ( b = ( ( 2s x.s m ) +s 1s ) -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = ( ( 2s x.s m ) +s 1s ) -> ( w = ( g +s ( b /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) ) ) with typecode |-
1364		breq1	Could not format ( b = ( ( 2s x.s m ) +s 1s ) -> ( b ( ( 2s x.s m ) +s 1s ) ( b ( ( 2s x.s m ) +s 1s )
1365	1363 1364	3anbi12d	Could not format ( b = ( ( 2s x.s m ) +s 1s ) -> ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s m ) +s 1s ) ( ( w = ( g +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s m ) +s 1s )
1366		oveq2	Could not format ( q = ( o +s 1s ) -> ( 2s ^su q ) = ( 2s ^su ( o +s 1s ) ) ) : No typesetting found for |- ( q = ( o +s 1s ) -> ( 2s ^su q ) = ( 2s ^su ( o +s 1s ) ) ) with typecode |-
1367	1366	oveq2d	Could not format ( q = ( o +s 1s ) -> ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) = ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) : No typesetting found for |- ( q = ( o +s 1s ) -> ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) = ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) with typecode |-
1368	1367	oveq2d	Could not format ( q = ( o +s 1s ) -> ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) : No typesetting found for |- ( q = ( o +s 1s ) -> ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) with typecode |-
1369	1368	eqeq2d	Could not format ( q = ( o +s 1s ) -> ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) ) : No typesetting found for |- ( q = ( o +s 1s ) -> ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) <-> w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) ) ) with typecode |-
1370	1366	breq2d	Could not format ( q = ( o +s 1s ) -> ( ( ( 2s x.s m ) +s 1s ) ( ( 2s x.s m ) +s 1s ) ( ( ( 2s x.s m ) +s 1s ) ( ( 2s x.s m ) +s 1s )
1371		oveq2	$$⊢q=o{+}_s{1}_s\to g{+}_{s}q=g{+}_s\left(o{+}_s{1}_s\right)$$
1372	1371	breq1d	$$⊢q=o{+}_s{1}_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s\left(o{+}_s{1}_s\right)\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
1373	1369 1370 1372	3anbi123d	Could not format ( q = ( o +s 1s ) -> ( ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s m ) +s 1s ) ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) /\ ( ( 2s x.s m ) +s 1s ) ( ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su q ) ) ) /\ ( ( 2s x.s m ) +s 1s ) ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) /\ ( ( 2s x.s m ) +s 1s )
1374	552 1365 1373	rspc3ev	Could not format ( ( ( g e. NN0_s /\ ( ( 2s x.s m ) +s 1s ) e. NN0_s /\ ( o +s 1s ) e. NN0_s ) /\ ( w = ( g +s ( ( ( 2s x.s m ) +s 1s ) /su ( 2s ^su ( o +s 1s ) ) ) ) /\ ( ( 2s x.s m ) +s 1s ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1375	1160 1165 1168 1330 1350 1360 1374	syl33anc	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1376	1375	expr	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( m E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( m E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1377	1376	rexlimdvvva	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. m e. NN0_s E. n e. NN0_s E. o e. NN0_s ( ( m E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1378	1158 1377	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1379	1378	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( h /su ( 2s ^su i ) ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( h /su ( 2s ^su i ) ) E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1380	963 1379	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1381	1380	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g = j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( g = j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1382	946 1381	jaod	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( g E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( g E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1383	645 1382	sylbid	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g <_s j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( g <_s j -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1384	643 1383	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1385	1384	expr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g <_s c -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( g <_s c -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1386	617 1385	mpd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1387	1386	ex	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( d E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1388	596 1387	mpd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1389	1388	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1390	1389	rexlimdvvva	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1391	273	3adant3	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` d ) C_ ( bday ` N ) ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( bday ` d ) C_ ( bday ` N ) ) with typecode |-
1392	59	a1i	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s\in \mathrm{No}$$
1393	124	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to w\in \mathrm{No}$$
1394		simp1r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{<}_{s}w$$
1395	1393 1394	0elleft	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s\in L\left(w\right)$$
1396	215 192 1395	rspcdva	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{\le }_{s}c$$
1397	1392 344 393 1396 285	slelttrd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{<}_{s}d$$
1398	1392 393 1397	sltled	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{\le }_{s}d$$
1399	1398	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s d ) : No typesetting found for |- ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s <_s d ) with typecode |-
1400		fveq2	$$⊢z=d\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(d\right)$$
1401	1400	sseq1d	$$⊢z=d\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
1402		breq2	$$⊢z=d\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}d\right)$$
1403	1401 1402	anbi12d	$$⊢z=d\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}d\right)\right)$$
1404		eqeq1	$$⊢z=d\to \left(z=N\leftrightarrow d=N\right)$$
1405		eqeq1	Could not format ( z = d -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> d = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( z = d -> ( z = ( x +s ( y /su ( 2s ^su p ) ) ) <-> d = ( x +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
1406	1405	3anbi1d	Could not format ( z = d -> ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
1407	1406	rexbidv	Could not format ( z = d -> ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
1408	1407	2rexbidv	Could not format ( z = d -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
1409		oveq1	Could not format ( x = j -> ( x +s ( y /su ( 2s ^su p ) ) ) = ( j +s ( y /su ( 2s ^su p ) ) ) ) : No typesetting found for |- ( x = j -> ( x +s ( y /su ( 2s ^su p ) ) ) = ( j +s ( y /su ( 2s ^su p ) ) ) ) with typecode |-
1410	1409	eqeq2d	Could not format ( x = j -> ( d = ( x +s ( y /su ( 2s ^su p ) ) ) <-> d = ( j +s ( y /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( x = j -> ( d = ( x +s ( y /su ( 2s ^su p ) ) ) <-> d = ( j +s ( y /su ( 2s ^su p ) ) ) ) ) with typecode |-
1411		oveq1	$$⊢x=j\to x{+}_{s}p=j{+}_{s}p$$
1412	1411	breq1d	$$⊢x=j\to \left(\left(x{+}_{s}p\right){<}_{s}N\leftrightarrow \left(j{+}_{s}p\right){<}_{s}N\right)$$
1413	1410 1412	3anbi13d	Could not format ( x = j -> ( ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y
1414	1413	rexbidv	Could not format ( x = j -> ( E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y ( E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y
1415		oveq1	Could not format ( y = k -> ( y /su ( 2s ^su p ) ) = ( k /su ( 2s ^su p ) ) ) : No typesetting found for |- ( y = k -> ( y /su ( 2s ^su p ) ) = ( k /su ( 2s ^su p ) ) ) with typecode |-
1416	1415	oveq2d	Could not format ( y = k -> ( j +s ( y /su ( 2s ^su p ) ) ) = ( j +s ( k /su ( 2s ^su p ) ) ) ) : No typesetting found for |- ( y = k -> ( j +s ( y /su ( 2s ^su p ) ) ) = ( j +s ( k /su ( 2s ^su p ) ) ) ) with typecode |-
1417	1416	eqeq2d	Could not format ( y = k -> ( d = ( j +s ( y /su ( 2s ^su p ) ) ) <-> d = ( j +s ( k /su ( 2s ^su p ) ) ) ) ) : No typesetting found for |- ( y = k -> ( d = ( j +s ( y /su ( 2s ^su p ) ) ) <-> d = ( j +s ( k /su ( 2s ^su p ) ) ) ) ) with typecode |-
1418		breq1	Could not format ( y = k -> ( y k ( y k
1419	1417 1418	3anbi12d	Could not format ( y = k -> ( ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k ( ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k
1420	1419	rexbidv	Could not format ( y = k -> ( E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k ( E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y E. p e. NN0_s ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k
1421		oveq2	Could not format ( p = l -> ( 2s ^su p ) = ( 2s ^su l ) ) : No typesetting found for |- ( p = l -> ( 2s ^su p ) = ( 2s ^su l ) ) with typecode |-
1422	1421	oveq2d	Could not format ( p = l -> ( k /su ( 2s ^su p ) ) = ( k /su ( 2s ^su l ) ) ) : No typesetting found for |- ( p = l -> ( k /su ( 2s ^su p ) ) = ( k /su ( 2s ^su l ) ) ) with typecode |-
1423	1422	oveq2d	Could not format ( p = l -> ( j +s ( k /su ( 2s ^su p ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) : No typesetting found for |- ( p = l -> ( j +s ( k /su ( 2s ^su p ) ) ) = ( j +s ( k /su ( 2s ^su l ) ) ) ) with typecode |-
1424	1423	eqeq2d	Could not format ( p = l -> ( d = ( j +s ( k /su ( 2s ^su p ) ) ) <-> d = ( j +s ( k /su ( 2s ^su l ) ) ) ) ) : No typesetting found for |- ( p = l -> ( d = ( j +s ( k /su ( 2s ^su p ) ) ) <-> d = ( j +s ( k /su ( 2s ^su l ) ) ) ) ) with typecode |-
1425	1421	breq2d	Could not format ( p = l -> ( k k ( k k
1426		oveq2	$$⊢p=l\to j{+}_{s}p=j{+}_{s}l$$
1427	1426	breq1d	$$⊢p=l\to \left(\left(j{+}_{s}p\right){<}_{s}N\leftrightarrow \left(j{+}_{s}l\right){<}_{s}N\right)$$
1428	1424 1425 1427	3anbi123d	Could not format ( p = l -> ( ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1429	1428	cbvrexvw	Could not format ( E. p e. NN0_s ( d = ( j +s ( k /su ( 2s ^su p ) ) ) /\ k E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1430	1420 1429	bitrdi	Could not format ( y = k -> ( E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( E. p e. NN0_s ( d = ( j +s ( y /su ( 2s ^su p ) ) ) /\ y E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1431	1414 1430	cbvrex2vw	Could not format ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( d = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1432	1408 1431	bitrdi	Could not format ( z = d -> ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1433	1404 1432	orbi12d	Could not format ( z = d -> ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1434	1403 1433	imbi12d	Could not format ( z = d -> ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` d ) C_ ( bday ` N ) /\ 0s <_s d ) -> ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y ( ( ( bday ` d ) C_ ( bday ` N ) /\ 0s <_s d ) -> ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1435	302 2	syl	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y A. z e. No ( ( ( bday ` z ) C_ ( bday ` N ) /\ 0s <_s z ) -> ( z = N \/ E. x e. NN0_s E. y e. NN0_s E. p e. NN0_s ( z = ( x +s ( y /su ( 2s ^su p ) ) ) /\ y
1436	1434 1435 394	rspcdva	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( bday ` d ) C_ ( bday ` N ) /\ 0s <_s d ) -> ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( ( ( bday ` d ) C_ ( bday ` N ) /\ 0s <_s d ) -> ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1437	1391 1399 1436	mp2and	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k ( d = N \/ E. j e. NN0_s E. k e. NN0_s E. l e. NN0_s ( d = ( j +s ( k /su ( 2s ^su l ) ) ) /\ k
1438	578 1390 1437	mpjaod	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1439	1438	3expa	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1440	1439	expr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1441	1440	rexlimdvvva	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. g e. NN0_s E. h e. NN0_s E. i e. NN0_s ( c = ( g +s ( h /su ( 2s ^su i ) ) ) /\ h E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1442	293 1441	syld	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` c ) C_ ( bday ` N ) /\ 0s <_s c ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1443	214 219 1442	mp2and	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1444	1443	ex	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( w = ( { c } |s { d } ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( { c } |s { d } ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1445	195 1444	mpd	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1446	1445	3expa	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1447	1446	expr	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( A. f e. ( _Right ` w ) d <_s f -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( A. f e. ( _Right ` w ) d <_s f -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1448	190 1447	sylbird	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( A. f e. ( _Right ` w ) -. f E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( A. f e. ( _Right ` w ) -. f E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1449	1448	rexlimdva	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( E. d e. ( _Right ` w ) A. f e. ( _Right ` w ) -. f E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. d e. ( _Right ` w ) A. f e. ( _Right ` w ) -. f E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1450	184 1449	syl5	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( _Right ` w ) e. Fin /\ ( _Right ` w ) =/= (/) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( _Right ` w ) e. Fin /\ ( _Right ` w ) =/= (/) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1451	158 179 1450	mp2and	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1452	1451	expr	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( A. e e. ( _Left ` w ) e <_s c -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( A. e e. ( _Left ` w ) e <_s c -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1453	154 1452	sylbird	Could not format ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( A. e e. ( _Left ` w ) -. c E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( A. e e. ( _Left ` w ) -. c E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1454	1453	rexlimdva	Could not format ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( E. c e. ( _Left ` w ) A. e e. ( _Left ` w ) -. c E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. c e. ( _Left ` w ) A. e e. ( _Left ` w ) -. c E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1455	147 1454	syl5	Could not format ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( ( _Left ` w ) e. Fin /\ ( _Left ` w ) =/= (/) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( _Left ` w ) e. Fin /\ ( _Left ` w ) =/= (/) ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1456	141 1455	mpand	Could not format ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( ( _Left ` w ) =/= (/) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( _Left ` w ) =/= (/) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1457	127 1456	mpd	Could not format ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1458	1457	ex	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) -> ( 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1459		id	$$⊢\phi \to \phi$$
1460		n0p1nns	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to N{+}_s{1}_s\in {\mathbb{N}}_s$$
1461	1 1460	syl	$$⊢\phi \to N{+}_s{1}_s\in {\mathbb{N}}_s$$
1462		nnsgt0	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_s\to 0_s{<}_s\left(N{+}_s{1}_s\right)$$
1463	1461 1462	syl	$$⊢\phi \to 0_s{<}_s\left(N{+}_s{1}_s\right)$$
1464		addslid	$$⊢0_s\in \mathrm{No}\to 0_s{+}_s{0}_s=0_s$$
1465	59 1464	ax-mp	$$⊢0_s{+}_s{0}_s=0_s$$
1466	1465	eqcomi	$$⊢0_s=0_s{+}_s{0}_s$$
1467	31 31 31	3pm3.2i	$$⊢\left(0_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge 0_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge 0_s\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
1468		oveq1	Could not format ( a = 0s -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( 0s +s ( b /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( a = 0s -> ( a +s ( b /su ( 2s ^su q ) ) ) = ( 0s +s ( b /su ( 2s ^su q ) ) ) ) with typecode |-
1469	1468	eqeq2d	Could not format ( a = 0s -> ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( a = 0s -> ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) ) ) with typecode |-
1470		oveq1	$$⊢a=0_s\to a{+}_{s}q=0_s{+}_{s}q$$
1471	1470	breq1d	$$⊢a=0_s\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(0_s{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
1472	1469 1471	3anbi13d	Could not format ( a = 0s -> ( ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) /\ b
1473	48	oveq2d	Could not format ( b = 0s -> ( 0s +s ( b /su ( 2s ^su q ) ) ) = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) ) : No typesetting found for |- ( b = 0s -> ( 0s +s ( b /su ( 2s ^su q ) ) ) = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) ) with typecode |-
1474	1473	eqeq2d	Could not format ( b = 0s -> ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( b = 0s -> ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) ) ) with typecode |-
1475	1474 51	3anbi12d	Could not format ( b = 0s -> ( ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( ( 0s = ( 0s +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s
1476	62	oveq2d	Could not format ( q = 0s -> ( 0s +s ( 0s /su ( 2s ^su q ) ) ) = ( 0s +s 0s ) ) : No typesetting found for |- ( q = 0s -> ( 0s +s ( 0s /su ( 2s ^su q ) ) ) = ( 0s +s 0s ) ) with typecode |-
1477	1476	eqeq2d	Could not format ( q = 0s -> ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s 0s ) ) ) : No typesetting found for |- ( q = 0s -> ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) <-> 0s = ( 0s +s 0s ) ) ) with typecode |-
1478		oveq2	$$⊢q=0_s\to 0_s{+}_{s}q=0_s{+}_s{0}_s$$
1479	1478 1465	eqtrdi	$$⊢q=0_s\to 0_s{+}_{s}q=0_s$$
1480	1479	breq1d	$$⊢q=0_s\to \left(\left(0_s{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow 0_s{<}_s\left(N{+}_s{1}_s\right)\right)$$
1481	1477 65 1480	3anbi123d	Could not format ( q = 0s -> ( ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( 0s = ( 0s +s 0s ) /\ 0s ( ( 0s = ( 0s +s ( 0s /su ( 2s ^su q ) ) ) /\ 0s ( 0s = ( 0s +s 0s ) /\ 0s
1482	1472 1475 1481	rspc3ev	Could not format ( ( ( 0s e. NN0_s /\ 0s e. NN0_s /\ 0s e. NN0_s ) /\ ( 0s = ( 0s +s 0s ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1483	1467 1482	mpan	Could not format ( ( 0s = ( 0s +s 0s ) /\ 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1484	1466 38 1483	mp3an12	Could not format ( 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1485	1463 1484	syl	Could not format ( ph -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1486	1459 1485	syl	Could not format ( ph -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1487		eqeq1	Could not format ( 0s = w -> ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( a +s ( b /su ( 2s ^su q ) ) ) ) ) : No typesetting found for |- ( 0s = w -> ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) <-> w = ( a +s ( b /su ( 2s ^su q ) ) ) ) ) with typecode |-
1488	1487	3anbi1d	Could not format ( 0s = w -> ( ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1489	1488	rexbidv	Could not format ( 0s = w -> ( E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1490	1489	2rexbidv	Could not format ( 0s = w -> ( E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( 0s = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1491	1486 1490	syl5ibcom	Could not format ( ph -> ( 0s = w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1492	1491	adantr	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) -> ( 0s = w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s = w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1493	1458 1492	jaod	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) -> ( ( 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( 0s E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1494	123 1493	sylbid	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) -> ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1495	1494	expr	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) -> ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) -> ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1496	1495	expd	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( w =/= ( N +s 1s ) -> ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( w =/= ( N +s 1s ) -> ( 0s <_s w -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1497	1496	com34	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1498	1497	impd	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1499	1498	impr	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) ) ) -> ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w =/= ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1500	120 1499	biimtrrid	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) ) ) -> ( -. w = ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( -. w = ( N +s 1s ) -> E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1501	1500	orrd	Could not format ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) ) ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1502	1501	expr	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1503	1502	expd	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1504	119 1503	sylbird	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) = suc ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) = suc ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1505	118 1504	jaod	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) C_ ( bday ` N ) \/ ( bday ` w ) = suc ( bday ` N ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) C_ ( bday ` N ) \/ ( bday ` w ) = suc ( bday ` N ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1506	16 1505	biimtrid	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) C_ suc ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) C_ suc ( bday ` N ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1507	6 1506	sylbid	Could not format ( ( ph /\ w e. No ) -> ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) -> ( 0s <_s w -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1508	1507	impd	Could not format ( ( ph /\ w e. No ) -> ( ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b ( ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b
1509	1508	ralrimiva	Could not format ( ph -> A. w e. No ( ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b A. w e. No ( ( ( bday ` w ) C_ ( bday ` ( N +s 1s ) ) /\ 0s <_s w ) -> ( w = ( N +s 1s ) \/ E. a e. NN0_s E. b e. NN0_s E. q e. NN0_s ( w = ( a +s ( b /su ( 2s ^su q ) ) ) /\ b