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		bdayon	$$⊢\mathrm{bday}\left(w\right)\in \mathrm{On}$$
8		bdayon	$$⊢\mathrm{bday}\left(N\right)\in \mathrm{On}$$
9	8	onsuci	$$⊢\mathrm{suc}\mathrm{bday}\left(N\right)\in \mathrm{On}$$
10	7 9	onsseli	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
11		onsssuc	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
12	7 8 11	mp2an	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
13	12	orbi1i	$$⊢\left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
14	10 13	bitr4i	$$⊢\mathrm{bday}\left(w\right)\subseteq \mathrm{suc}\mathrm{bday}\left(N\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\vee \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
15		fveq2	$$⊢z=w\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(w\right)$$
16	15	sseq1d	$$⊢z=w\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
17		breq2	$$⊢z=w\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}w\right)$$
18	16 17	anbi12d	$$⊢z=w\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(w\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}w\right)\right)$$
19		eqeq1	$$⊢z=w\to \left(z=N\leftrightarrow w=N\right)$$
20		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 |-
21	20	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
22	21	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
23	22	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
24	19 23	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
25	18 24	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
26	25	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
27	2 26	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
28	1	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
29		0n0s	$$⊢0_s\in {\mathbb{N}}_{\mathrm{0s}}$$
30	29	a1i	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to 0_s\in {\mathbb{N}}_{\mathrm{0s}}$$
31		simprr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to w=N$$
32	1	n0nod	$$⊢\phi \to N\in \mathrm{No}$$
33	32	addsridd	$$⊢\phi \to N{+}_s{0}_s=N$$
34	33	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to N{+}_s{0}_s=N$$
35	31 34	eqtr4d	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to w=N{+}_s{0}_s$$
36		0lt1s	$$⊢0_s{<}_s{1}_s$$
37	36	a1i	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to 0_s{<}_s{1}_s$$
38	32	ltsp1d	$$⊢\phi \to N{<}_s\left(N{+}_s{1}_s\right)$$
39	33 38	eqbrtrd	$$⊢\phi \to \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)$$
40	39	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge w=N\right)\right)\to \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)$$
41		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 |-
42	41	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 |-
43		oveq1	$$⊢a=N\to a{+}_{s}q=N{+}_{s}q$$
44	43	breq1d	$$⊢a=N\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(N{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
45	42 44	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
46		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 |-
47	46	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 |-
48	47	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 |-
49		breq1	Could not format ( b = 0s -> ( b 0s ( b 0s
50	48 49	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
51		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 |-
52		2no	Could not format 2s e. No : No typesetting found for |- 2s e. No with typecode |-
53		exps0	Could not format ( 2s e. No -> ( 2s ^su 0s ) = 1s ) : No typesetting found for |- ( 2s e. No -> ( 2s ^su 0s ) = 1s ) with typecode |-
54	52 53	ax-mp	Could not format ( 2s ^su 0s ) = 1s : No typesetting found for |- ( 2s ^su 0s ) = 1s with typecode |-
55	51 54	eqtrdi	Could not format ( q = 0s -> ( 2s ^su q ) = 1s ) : No typesetting found for |- ( q = 0s -> ( 2s ^su q ) = 1s ) with typecode |-
56	55	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 |-
57		0no	$$⊢0_s\in \mathrm{No}$$
58		divs1	$$⊢0_s\in \mathrm{No}\to 0_s{/}_{\mathrm{su}}{1}_s=0_s$$
59	57 58	ax-mp	$$⊢0_s{/}_{\mathrm{su}}{1}_s=0_s$$
60	56 59	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 |-
61	60	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 |-
62	61	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 |-
63	55	breq2d	Could not format ( q = 0s -> ( 0s 0s ( 0s 0s
64		oveq2	$$⊢q=0_s\to N{+}_{s}q=N{+}_s{0}_s$$
65	64	breq1d	$$⊢q=0_s\to \left(\left(N{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(N{+}_s{0}_s\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
66	62 63 65	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
67	45 50 66	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
68	28 30 30 35 37 40 67	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
69	68	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
70		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 |-
71		idd	Could not format ( ( ph /\ ( x e. NN0_s /\ y e. NN0_s /\ p e. NN0_s ) ) -> ( y y ( y y
72		n0addscl	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in {\mathbb{N}}_{\mathrm{0s}}$$
73	72	n0nod	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in \mathrm{No}$$
74	73	3adant2	$$⊢\left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\to x{+}_{s}p\in \mathrm{No}$$
75	74	adantl	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to x{+}_{s}p\in \mathrm{No}$$
76	75	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to x{+}_{s}p\in \mathrm{No}$$
77	32	adantr	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to N\in \mathrm{No}$$
78	77	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N\in \mathrm{No}$$
79		peano2no	$$⊢N\in \mathrm{No}\to N{+}_s{1}_s\in \mathrm{No}$$
80	78 79	syl	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N{+}_s{1}_s\in \mathrm{No}$$
81		simpr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to \left(x{+}_{s}p\right){<}_{s}N$$
82	77	ltsp1d	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to N{<}_s\left(N{+}_s{1}_s\right)$$
83	82	adantr	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to N{<}_s\left(N{+}_s{1}_s\right)$$
84	76 78 80 81 83	ltstrd	$$⊢\left(\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\wedge \left(x{+}_{s}p\right){<}_{s}N\right)\to \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)$$
85	84	ex	$$⊢\left(\phi \wedge \left(x\in {\mathbb{N}}_{\mathrm{0s}}\wedge y\in {\mathbb{N}}_{\mathrm{0s}}\wedge p\in {\mathbb{N}}_{\mathrm{0s}}\right)\right)\to \left(\left(x{+}_{s}p\right){<}_{s}N\to \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
86	70 71 85	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
87		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 |-
88	87	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 |-
89		oveq1	$$⊢a=x\to a{+}_{s}q=x{+}_{s}q$$
90	89	breq1d	$$⊢a=x\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(x{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
91	88 90	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
92		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 |-
93	92	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 |-
94	93	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 |-
95		breq1	Could not format ( b = y -> ( b y ( b y
96	94 95	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
97		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 |-
98	97	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 |-
99	98	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 |-
100	99	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 |-
101	97	breq2d	Could not format ( q = p -> ( y y ( y y
102		oveq2	$$⊢q=p\to x{+}_{s}q=x{+}_{s}p$$
103	102	breq1d	$$⊢q=p\to \left(\left(x{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(x{+}_{s}p\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
104	100 101 103	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
105	91 96 104	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
106	105	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
107	106	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
108	86 107	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
109	108	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
110	109	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
111	69 110	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
112	27 111	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
113	112	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
114	113	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
115	114	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
116	115	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
117	5	eqeq2d	$$⊢\left(\phi \wedge w\in \mathrm{No}\right)\to \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
118		df-ne	$$⊢w\ne N{+}_s{1}_s\leftrightarrow \neg w=N{+}_s{1}_s$$
119		simprl	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to w\in \mathrm{No}$$
120		lesloe	$$⊢\left(0_s\in \mathrm{No}\wedge w\in \mathrm{No}\right)\to \left(0_s{\le }_{s}w\leftrightarrow \left(0_s{<}_{s}w\vee 0_s=w\right)\right)$$
121	57 119 120	sylancr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \left(0_s{\le }_{s}w\leftrightarrow \left(0_s{<}_{s}w\vee 0_s=w\right)\right)$$
122		simprrl	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
123	122	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
124	1	peano2n0sd	$$⊢\phi \to N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
125		n0bday	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
126	124 125	syl	$$⊢\phi \to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
127	126	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
128	127	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{\omega }$$
129	123 128	eqeltrd	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{bday}\left(w\right)\in \mathrm{\omega }$$
130		oldfi	$$⊢\mathrm{bday}\left(w\right)\in \mathrm{\omega }\to \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}$$
131	129 130	syl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}$$
132		leftssold	$$⊢L\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
133		ssfi	$$⊢\left(\mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}\wedge L\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\right)\to L\left(w\right)\in \mathrm{Fin}$$
134	131 132 133	sylancl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to L\left(w\right)\in \mathrm{Fin}$$
135		simplrl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to w\in \mathrm{No}$$
136		simpr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to 0_s{<}_{s}w$$
137	135 136	0elleft	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to 0_s\in L\left(w\right)$$
138	137	ne0d	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to L\left(w\right)\ne \varnothing$$
139		leftssno	$$⊢L\left(w\right)\subseteq \mathrm{No}$$
140		ltsso	$$⊢{<}_s\mathrm{Or}\mathrm{No}$$
141		soss	$$⊢L\left(w\right)\subseteq \mathrm{No}\to \left({<}_s\mathrm{Or}\mathrm{No}\to {<}_s\mathrm{Or}L\left(w\right)\right)$$
142	139 140 141	mp2	$$⊢{<}_s\mathrm{Or}L\left(w\right)$$
143		fimax2g	$$⊢\left({<}_s\mathrm{Or}L\left(w\right)\wedge L\left(w\right)\in \mathrm{Fin}\wedge L\left(w\right)\ne \varnothing \right)\to \exists c\in L\left(w\right)\forall e\in L\left(w\right)\neg c{<}_{s}e$$
144	142 143	mp3an1	$$⊢\left(L\left(w\right)\in \mathrm{Fin}\wedge L\left(w\right)\ne \varnothing \right)\to \exists c\in L\left(w\right)\forall e\in L\left(w\right)\neg c{<}_{s}e$$
145		leftno	$$⊢e\in L\left(w\right)\to e\in \mathrm{No}$$
146		leftno	$$⊢c\in L\left(w\right)\to c\in \mathrm{No}$$
147		lenlts	$$⊢\left(e\in \mathrm{No}\wedge c\in \mathrm{No}\right)\to \left(e{\le }_{s}c\leftrightarrow \neg c{<}_{s}e\right)$$
148	145 146 147	syl2anr	$$⊢\left(c\in L\left(w\right)\wedge e\in L\left(w\right)\right)\to \left(e{\le }_{s}c\leftrightarrow \neg c{<}_{s}e\right)$$
149	148	ralbidva	$$⊢c\in L\left(w\right)\to \left(\forall e\in L\left(w\right)e{\le }_{s}c\leftrightarrow \forall e\in L\left(w\right)\neg c{<}_{s}e\right)$$
150	149	adantl	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge c\in L\left(w\right)\right)\to \left(\forall e\in L\left(w\right)e{\le }_{s}c\leftrightarrow \forall e\in L\left(w\right)\neg c{<}_{s}e\right)$$
151		rightssold	$$⊢R\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
152		ssfi	$$⊢\left(\mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\in \mathrm{Fin}\wedge R\left(w\right)\subseteq \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\right)\to R\left(w\right)\in \mathrm{Fin}$$
153	131 151 152	sylancl	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to R\left(w\right)\in \mathrm{Fin}$$
154	153	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to R\left(w\right)\in \mathrm{Fin}$$
155	135	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to w\in \mathrm{No}$$
156		simprrr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to w\ne N{+}_s{1}_s$$
157	156	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to w\ne N{+}_s{1}_s$$
158	157	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to w\ne N{+}_s{1}_s$$
159	158	neneqd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg w=N{+}_s{1}_s$$
160		simpr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to w\in {On}_s$$
161	124	ad4antr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
162		n0on	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to N{+}_s{1}_s\in {On}_s$$
163	161 162	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to N{+}_s{1}_s\in {On}_s$$
164	123	adantr	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
165	164	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
166		bday11on	$$⊢\left(w\in {On}_s\wedge N{+}_s{1}_s\in {On}_s\wedge \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\right)\to w=N{+}_s{1}_s$$
167	160 163 165 166	syl3anc	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge w\in {On}_s\right)\to w=N{+}_s{1}_s$$
168	159 167	mtand	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg w\in {On}_s$$
169		elons	$$⊢w\in {On}_s\leftrightarrow \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
170	169	notbii	$$⊢\neg w\in {On}_s\leftrightarrow \neg \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
171		imnan	$$⊢\left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)\leftrightarrow \neg \left(w\in \mathrm{No}\wedge R\left(w\right)=\varnothing \right)$$
172	170 171	bitr4i	$$⊢\neg w\in {On}_s\leftrightarrow \left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)$$
173	168 172	sylib	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \left(w\in \mathrm{No}\to \neg R\left(w\right)=\varnothing \right)$$
174	155 173	mpd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to \neg R\left(w\right)=\varnothing$$
175	174	neqned	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\to R\left(w\right)\ne \varnothing$$
176		rightssno	$$⊢R\left(w\right)\subseteq \mathrm{No}$$
177		soss	$$⊢R\left(w\right)\subseteq \mathrm{No}\to \left({<}_s\mathrm{Or}\mathrm{No}\to {<}_s\mathrm{Or}R\left(w\right)\right)$$
178	176 140 177	mp2	$$⊢{<}_s\mathrm{Or}R\left(w\right)$$
179		fimin2g	$$⊢\left({<}_s\mathrm{Or}R\left(w\right)\wedge R\left(w\right)\in \mathrm{Fin}\wedge R\left(w\right)\ne \varnothing \right)\to \exists d\in R\left(w\right)\forall f\in R\left(w\right)\neg f{<}_{s}d$$
180	178 179	mp3an1	$$⊢\left(R\left(w\right)\in \mathrm{Fin}\wedge R\left(w\right)\ne \varnothing \right)\to \exists d\in R\left(w\right)\forall f\in R\left(w\right)\neg f{<}_{s}d$$
181		rightno	$$⊢d\in R\left(w\right)\to d\in \mathrm{No}$$
182		rightno	$$⊢f\in R\left(w\right)\to f\in \mathrm{No}$$
183		lenlts	$$⊢\left(d\in \mathrm{No}\wedge f\in \mathrm{No}\right)\to \left(d{\le }_{s}f\leftrightarrow \neg f{<}_{s}d\right)$$
184	181 182 183	syl2an	$$⊢\left(d\in R\left(w\right)\wedge f\in R\left(w\right)\right)\to \left(d{\le }_{s}f\leftrightarrow \neg f{<}_{s}d\right)$$
185	184	ralbidva	$$⊢d\in R\left(w\right)\to \left(\forall f\in R\left(w\right)d{\le }_{s}f\leftrightarrow \forall f\in R\left(w\right)\neg f{<}_{s}d\right)$$
186	185	adantl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\right)\wedge d\in R\left(w\right)\right)\to \left(\forall f\in R\left(w\right)d{\le }_{s}f\leftrightarrow \forall f\in R\left(w\right)\neg f{<}_{s}d\right)$$
187		simp2l	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c\in L\left(w\right)$$
188		simp2r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \forall e\in L\left(w\right)e{\le }_{s}c$$
189		simp3l	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to d\in R\left(w\right)$$
190		simp3r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \forall f\in R\left(w\right)d{\le }_{s}f$$
191	187 188 189 190	cutminmax	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to w=\left\{c\right\}{|}_s\left\{d\right\}$$
192		simpl2l	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in L\left(w\right)$$
193	132 192	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
194	192	leftnod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c\in \mathrm{No}$$
195		oldbday	$$⊢\left(\mathrm{bday}\left(w\right)\in \mathrm{On}\wedge c\in \mathrm{No}\right)\to \left(c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)\right)$$
196	7 194 195	sylancr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(c\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)\right)$$
197	193 196	mpbid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\in \mathrm{bday}\left(w\right)$$
198	123	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
199	198	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)$$
200	1	adantr	$$⊢\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
201	200	adantr	$$⊢\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
202	201	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
203	202	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in {\mathbb{N}}_{\mathrm{0s}}$$
204	203 3	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(N{+}_s{1}_s\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
205	199 204	eqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(w\right)=\mathrm{suc}\mathrm{bday}\left(N\right)$$
206	197 205	eleqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
207		bdayon	$$⊢\mathrm{bday}\left(c\right)\in \mathrm{On}$$
208		onsssuc	$$⊢\left(\mathrm{bday}\left(c\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
209	207 8 208	mp2an	$$⊢\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
210	206 209	sylibr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)$$
211		breq1	$$⊢e=0_s\to \left(e{\le }_{s}c\leftrightarrow 0_s{\le }_{s}c\right)$$
212		simpl2r	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \forall e\in L\left(w\right)e{\le }_{s}c$$
213		simpl1	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)$$
214	213 137	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to 0_s\in L\left(w\right)$$
215	211 212 214	rspcdva	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to 0_s{\le }_{s}c$$
216		simp1ll	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to \phi$$
217	216	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \phi$$
218		n0on	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to N\in {On}_s$$
219	1 218	syl	$$⊢\phi \to N\in {On}_s$$
220	217 219	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in {On}_s$$
221		simpl3l	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in R\left(w\right)$$
222	151 221	sselid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)$$
223		oldbdayim	$$⊢d\in \mathrm{Old}\left(\mathrm{bday}\left(w\right)\right)\to \mathrm{bday}\left(d\right)\in \mathrm{bday}\left(w\right)$$
224	222 223	syl	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\in \mathrm{bday}\left(w\right)$$
225	224 205	eleqtrd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
226		bdayon	$$⊢\mathrm{bday}\left(d\right)\in \mathrm{On}$$
227		onsssuc	$$⊢\left(\mathrm{bday}\left(d\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)\right)$$
228	226 8 227	mp2an	$$⊢\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\in \mathrm{suc}\mathrm{bday}\left(N\right)$$
229	225 228	sylibr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)$$
230	221	rightnod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in \mathrm{No}$$
231		madebday	$$⊢\left(\mathrm{bday}\left(N\right)\in \mathrm{On}\wedge d\in \mathrm{No}\right)\to \left(d\in M\left(\mathrm{bday}\left(N\right)\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
232	8 230 231	sylancr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(d\in M\left(\mathrm{bday}\left(N\right)\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
233	229 232	mpbird	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d\in M\left(\mathrm{bday}\left(N\right)\right)$$
234		onsbnd	$$⊢\left(N\in {On}_s\wedge d\in M\left(\mathrm{bday}\left(N\right)\right)\right)\to d{\le }_{s}N$$
235	220 233 234	syl2anc	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to d{\le }_{s}N$$
236	203	n0nod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to N\in \mathrm{No}$$
237	230 236	lesnltd	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(d{\le }_{s}N\leftrightarrow \neg N{<}_{s}d\right)$$
238	235 237	mpbid	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \neg N{<}_{s}d$$
239		lltr	$$⊢L\left(w\right){\ll }_{s}R\left(w\right)$$
240	239	a1i	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to L\left(w\right){\ll }_{s}R\left(w\right)$$
241	240 187 189	sltssepcd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c{<}_{s}d$$
242	241	adantr	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to c{<}_{s}d$$
243		breq1	$$⊢c=N\to \left(c{<}_{s}d\leftrightarrow N{<}_{s}d\right)$$
244	242 243	syl5ibcom	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \left(c=N\to N{<}_{s}d\right)$$
245	238 244	mtod	$$⊢\left(\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\wedge w=\left\{c\right\}{|}_s\left\{d\right\}\right)\to \neg c=N$$
246		fveq2	$$⊢z=c\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(c\right)$$
247	246	sseq1d	$$⊢z=c\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
248		breq2	$$⊢z=c\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}c\right)$$
249	247 248	anbi12d	$$⊢z=c\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(c\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}c\right)\right)$$
250		eqeq1	$$⊢z=c\to \left(z=N\leftrightarrow c=N\right)$$
251		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 |-
252	251	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
253	252	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
254	253	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
255		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 |-
256	255	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 |-
257		oveq1	$$⊢x=g\to x{+}_{s}p=g{+}_{s}p$$
258	257	breq1d	$$⊢x=g\to \left(\left(x{+}_{s}p\right){<}_{s}N\leftrightarrow \left(g{+}_{s}p\right){<}_{s}N\right)$$
259	256 258	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
260	259	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
261		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 |-
262	261	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 |-
263	262	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 |-
264		breq1	Could not format ( y = h -> ( y h ( y h
265	263 264	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
266	265	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
267		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 |-
268	267	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 |-
269	268	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 |-
270	269	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 |-
271	267	breq2d	Could not format ( p = i -> ( h h ( h h
272		oveq2	$$⊢p=i\to g{+}_{s}p=g{+}_{s}i$$
273	272	breq1d	$$⊢p=i\to \left(\left(g{+}_{s}p\right){<}_{s}N\leftrightarrow \left(g{+}_{s}i\right){<}_{s}N\right)$$
274	270 271 273	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
275	274	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
276	266 275	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
277	260 276	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
278	254 277	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
279	250 278	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
280	249 279	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
281	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
282	281	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
283	282	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
284	283	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
285	280 284 194	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
286		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
287	245 285 286	sylsyld	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
288		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 |-
289	288	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 |-
290	289	n0nod	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 |-
291		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 |-
292	291	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 |-
293		n0addscl	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge i\in {\mathbb{N}}_{\mathrm{0s}}\right)\to g{+}_{s}i\in {\mathbb{N}}_{\mathrm{0s}}$$
294	289 292 293	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 |-
295	294	n0nod	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 |-
296	216	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 |-
297	296	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 |-
298	297 32	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 |-
299		n0sge0	$$⊢i\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}i$$
300	292 299	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 |-
301	292	n0nod	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 |-
302	290 301	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 |-
303	300 302	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 |-
304		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 )
305	304	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 )
306	290 295 298 303 305	leltstrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
307	297 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 |-
308		n0ltsp1le	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{<}_{s}N\leftrightarrow \left(g{+}_s{1}_s\right){\le }_{s}N\right)$$
309	289 307 308	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 |-
310	306 309	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 |-
311		ltsirr	$$⊢N\in \mathrm{No}\to \neg N{<}_{s}N$$
312	298 311	syl	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s -. N -. N
313	289	peano2n0sd	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 |-
314	313	n0nod	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 |-
315	314 298	ltsnled	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 |-
316	296	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 |-
317	124	n0nod	$$⊢\phi \to N{+}_s{1}_s\in \mathrm{No}$$
318	316 317	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 |-
319	316 32	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 |-
320	52	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 |-
321	319 320	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 |-
322		1no	$$⊢1_s\in \mathrm{No}$$
323	322	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 |-
324	321 323 323	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 |-
325		1p1e2s	Could not format ( 1s +s 1s ) = 2s : No typesetting found for |- ( 1s +s 1s ) = 2s with typecode |-
326	325	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 |-
327		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 |-
328	319 52 327	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 |-
329	326 328	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 |-
330	324 329	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 |-
331	330 319	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 |-
332	321 323	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 |-
333	198	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 |-
334	333	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 |-
335		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 |-
336	187	leftnod	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to c\in \mathrm{No}$$
337	336	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 |-
338	337	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 |-
339	288	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 |-
340	339	peano2n0sd	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 |-
341	340	n0nod	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 |-
342		subscl	$$⊢\left(N\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to N{-}_s{1}_s\in \mathrm{No}$$
343	32 322 342	sylancl	$$⊢\phi \to N{-}_s{1}_s\in \mathrm{No}$$
344	316 343	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 |-
345		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 |-
346	345	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 |-
347		simp3r2	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
348	347	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
349	291	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 |-
350		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 |-
351	52 349 350	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 |-
352	351	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 |-
353	348 352	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
354		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 |-
355	354	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 |-
356	355	n0nod	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 |-
357	356 323 349	pw2ltdivmuls2d	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
358	353 357	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 ) )
359	356 349	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 |-
360	339	n0nod	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 |-
361	359 323 360	ltadds2d	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 ) ) )
362	358 361	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 ) ) )
363	346 362	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
364		n0ltsp1le	$$⊢\left(g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(\left(g{+}_s{1}_s\right){<}_{s}N\leftrightarrow \left(\left(g{+}_s{1}_s\right){+}_s{1}_s\right){\le }_{s}N\right)$$
365	313 307 364	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 |-
366	365	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 |-
367	366	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 |-
368		npcans	$$⊢\left(N\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(N{-}_s{1}_s\right){+}_s{1}_s=N$$
369	319 322 368	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 |-
370	367 369	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 |-
371	341 344 323	leadds1d	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 |-
372	370 371	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 |-
373	338 341 344 363 372	ltlestrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
374	325	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 |-
375	374	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 |-
376	319 323 323	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 |-
377	376	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 |-
378		npcans	$$⊢\left(N{-}_s{1}_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(\left(N{-}_s{1}_s\right){-}_s{1}_s\right){+}_s{1}_s=N{-}_s{1}_s$$
379	344 322 378	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 |-
380	377 379	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 |-
381	375 380	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 |-
382	373 381	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
383	338 332 382	sltssn	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
384	189	rightnod	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to d\in \mathrm{No}$$
385	384	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 |-
386	385	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 |-
387		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 |-
388	387	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 |-
389	386	ltsm1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( d -s 1s ) ( d -s 1s )
390	388 389	eqbrtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N -s 1s ) ( N -s 1s )
391	381 390	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 )
392	332 386 391	sltssn	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 ) } <
393	335 332 383 392	sltsbday	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 |-
394	334 393	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 |-
395	124 162	syl	$$⊢\phi \to N{+}_s{1}_s\in {On}_s$$
396	316 395	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 |-
397	319 323 320	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 |-
398		n0sge0	$$⊢g\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}g$$
399	339 398	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 |-
400	323 360	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 |-
401	399 400	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 |-
402	360 323	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 |-
403	401 402	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 |-
404		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 )
405	323 341 319 403 404	leltstrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s 1s
406	323 319 405	ltlesd	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 |-
407	323 319 323	leadds1d	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 |-
408	406 407	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 |-
409	325 408	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 |-
410		2nns	Could not format 2s e. NN_s : No typesetting found for |- 2s e. NN_s with typecode |-
411		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 |-
412	410 411	ax-mp	Could not format 2s e. NN0_s : No typesetting found for |- 2s e. NN0_s with typecode |-
413	296 124	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 |-
414	413	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 |-
415		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 |-
416	412 414 415	sylancr	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 |-
417	409 416	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 |-
418	397 417	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 |-
419		n0on	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 |-
420	418 419	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 |-
421	396 420	onlesd	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 |-
422	394 421	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 |-
423	332	ltsp1d	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 )
424	318 332 331 422 423	leltstrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( N +s 1s ) ( N +s 1s )
425	318 331 424	ltlesd	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 |-
426	425 330	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 |-
427	316 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 |-
428		n0ltsp1le	$$⊢\left(N\in {\mathbb{N}}_{\mathrm{0s}}\wedge N\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(N{<}_{s}N\leftrightarrow \left(N{+}_s{1}_s\right){\le }_{s}N\right)$$
429	427 427 428	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 |-
430	426 429	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
431	430	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
432	315 431	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
433	312 432	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 |-
434	314 298	lestri3d	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 |-
435	310 433 434	mpbir2and	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 |-
436	304	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 )
437		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 |-
438	436 437	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 )
439	291	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 |-
440	439	n0nod	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 |-
441	322	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 |-
442	288	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 |-
443	442	n0nod	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 |-
444	440 441 443	ltadds2d	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 )
445	438 444	mpbird	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s i i
446		n0lts1e0	$$⊢i\in {\mathbb{N}}_{\mathrm{0s}}\to \left(i{<}_s{1}_s\leftrightarrow i=0_s\right)$$
447	439 446	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 |-
448	445 447	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 |-
449	345	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 |-
450	347	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
451		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 |-
452	451	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 |-
453	452	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 |-
454	453 54	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 |-
455	450 454	breqtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
456	354	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 |-
457		n0lts1e0	$$⊢h\in {\mathbb{N}}_{\mathrm{0s}}\to \left(h{<}_s{1}_s\leftrightarrow h=0_s\right)$$
458	456 457	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 |-
459	455 458	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 |-
460	459 454	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 |-
461	460 59	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 |-
462	461	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 |-
463	288	n0nod	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 |-
464	463	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 |-
465	464	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 |-
466	449 462 465	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 |-
467		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 |-
468	54	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 |-
469	463	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 |-
470	469	divs1d	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 |-
471		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 |-
472	470 471	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 |-
473	468 472	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 |-
474	473	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 |-
475	54	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 |-
476		simpllr	$$⊢\left(\left(\left(d=N\wedge g{+}_s{1}_s=N\right)\wedge i=0_s\right)\wedge c=g\right)\to g{+}_s{1}_s=N$$
477	476	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 |-
478	288	peano2n0sd	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 |-
479	478	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 |-
480	479	n0nod	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 |-
481	480	divs1d	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 |-
482		simplll	$$⊢\left(\left(\left(d=N\wedge g{+}_s{1}_s=N\right)\wedge i=0_s\right)\wedge c=g\right)\to d=N$$
483	482	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 |-
484	477 481 483	3eqtr4d	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 |-
485	475 484	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 |-
486	485	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 |-
487	474 486	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 |-
488	288	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 |-
489	488	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 |-
490	29	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 |-
491	489 490	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 |-
492	467 487 491	3eqtr2d	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 |-
493		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 |-
494	52 469 493	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 |-
495	322	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 |-
496		addslid	$$⊢1_s\in \mathrm{No}\to 0_s{+}_s{1}_s=1_s$$
497	322 496	ax-mp	$$⊢0_s{+}_s{1}_s=1_s$$
498		1n0s	$$⊢1_s\in {\mathbb{N}}_{\mathrm{0s}}$$
499	497 498	eqeltri	$$⊢0_s{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}$$
500	499	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 |-
501	494 495 500	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 |-
502		exps1	Could not format ( 2s e. No -> ( 2s ^su 1s ) = 2s ) : No typesetting found for |- ( 2s e. No -> ( 2s ^su 1s ) = 2s ) with typecode |-
503	52 502	ax-mp	Could not format ( 2s ^su 1s ) = 2s : No typesetting found for |- ( 2s ^su 1s ) = 2s with typecode |-
504	503	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 |-
505	504	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 |-
506	498	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 |-
507	469 490 506	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 |-
508	468 507 470	3eqtr3a	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 |-
509	505 508	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 |-
510	497	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 |-
511	510 503	eqtri	Could not format ( 2s ^su ( 0s +s 1s ) ) = 2s : No typesetting found for |- ( 2s ^su ( 0s +s 1s ) ) = 2s with typecode |-
512	511	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 |-
513	512	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 |-
514	509 513	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 |-
515	501 514	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 |-
516	515	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 |-
517	288	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 |-
518	498	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 |-
519		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 |-
520		ltadds1	$$⊢\left(0_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(0_s{<}_s{1}_s\leftrightarrow \left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)\right)$$
521	57 322 322 520	mp3an	$$⊢0_s{<}_s{1}_s\leftrightarrow \left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)$$
522	36 521	mpbi	$$⊢\left(0_s{+}_s{1}_s\right){<}_s\left(1_s{+}_s{1}_s\right)$$
523	522 497 325	3brtr3i	Could not format 1s
524	523	a1i	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 1s 1s
525		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 |-
526	525	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 |-
527	296	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 |-
528	527 32	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 |-
529	528	ltsp1d	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
530	526 529	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 )
531		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 |-
532	531	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 |-
533		oveq1	$$⊢a=g\to a{+}_{s}q=g{+}_{s}q$$
534	533	breq1d	$$⊢a=g\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
535	532 534	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
536		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 |-
537	536	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 |-
538	537	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 |-
539		breq1	Could not format ( b = 1s -> ( b 1s ( b 1s
540	538 539	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
541		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 |-
542	541 503	eqtrdi	Could not format ( q = 1s -> ( 2s ^su q ) = 2s ) : No typesetting found for |- ( q = 1s -> ( 2s ^su q ) = 2s ) with typecode |-
543	542	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 |-
544	543	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 |-
545	544	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 |-
546	542	breq2d	Could not format ( q = 1s -> ( 1s 1s ( 1s 1s
547		oveq2	$$⊢q=1_s\to g{+}_{s}q=g{+}_s{1}_s$$
548	547	breq1d	$$⊢q=1_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s{1}_s\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
549	545 546 548	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
550	535 540 549	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
551	517 518 518 519 524 530 550	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
552	551	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
553	516 552	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
554	492 553	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
555	554	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
556	466 555	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
557	556	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
558	448 557	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
559	558	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
560	435 559	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
561	560	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
562		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 |-
563		simprr2	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
564		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 |-
565		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 |-
566	52 564 565	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 |-
567	566	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 |-
568	563 567	breqtrrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
569		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 |-
570	569	n0nod	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 |-
571	322	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 |-
572	570 571 564	pw2ltdivmuls2d	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
573	568 572	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 ) )
574	570 564	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 |-
575		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 |-
576	575	n0nod	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 |-
577	574 571 576	ltadds2d	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 ) ) )
578	573 577	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 ) ) )
579	562 578	eqbrtrd	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d d
580	288	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 |-
581	580	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 |-
582	581	n0nod	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 |-
583	582	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 |-
584	354	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 |-
585	584	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 |-
586		n0sge0	$$⊢h\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}h$$
587	585 586	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 |-
588	585	n0nod	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 |-
589	291	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 |-
590	589	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 |-
591	588 590	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 |-
592	57	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 |-
593	588 590	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 |-
594	592 593 582	leadds2d	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 |-
595	591 594	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 |-
596	587 595	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 |-
597	583 596	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 |-
598	345	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 |-
599	598	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 |-
600	597 599	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 |-
601	580	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 |-
602	601	n0nod	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 |-
603	337	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 |-
604	603	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 |-
605	385	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 |-
606	605	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 |-
607		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 |-
608	241	3ad2ant1	Could not format ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
609	608	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
610	609	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
611	602 604 606 607 610	leltstrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
612	580	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 |-
613	612	n0nod	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 |-
614	605	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 |-
615	575	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 |-
616	615	peano2n0sd	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 |-
617	616	n0nod	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 |-
618		simprr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
619		simprll	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s d d
620	613 614 617 618 619	ltstrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s g g
621		n0lesltp1	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge j\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{\le }_{s}j\leftrightarrow g{<}_s\left(j{+}_s{1}_s\right)\right)$$
622	612 615 621	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
623	620 622	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 |-
624	623	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 |-
625	611 624	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 |-
626	576	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 |-
627	602 626	lesloed	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
628	575	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 |-
629		n0ltsp1le	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge j\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(g{<}_{s}j\leftrightarrow \left(g{+}_s{1}_s\right){\le }_{s}j\right)$$
630	601 628 629	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 |-
631	630	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 |-
632	631	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 |-
633	478	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 |-
634	633	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 |-
635	634	n0nod	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 |-
636	575	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 |-
637	636	n0nod	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 |-
638	605	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 |-
639		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 |-
640	569	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 |-
641		n0sge0	$$⊢k\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}k$$
642	640 641	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 |-
643	640	n0nod	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 |-
644	564	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 |-
645	643 644	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 |-
646	643 644	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 |-
647	637 646	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 |-
648	645 647	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 |-
649	642 648	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 |-
650	562	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 |-
651	649 650	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 |-
652	635 637 638 639 651	lestrd	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 |-
653	575	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 |-
654	564	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 |-
655		n0addscl	$$⊢\left(j\in {\mathbb{N}}_{\mathrm{0s}}\wedge l\in {\mathbb{N}}_{\mathrm{0s}}\right)\to j{+}_{s}l\in {\mathbb{N}}_{\mathrm{0s}}$$
656	653 654 655	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 |-
657	656	n0nod	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 |-
658	296	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 |-
659	658	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 |-
660	659 32	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 |-
661	659 317	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 |-
662		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 )
663	662	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 )
664	660	ltsp1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s N N
665	657 660 661 663 664	ltstrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( j +s l ) ( j +s l )
666	657 661	ltsnled	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 |-
667	665 666	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 |-
668	633	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 |-
669	668	n0nod	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 |-
670	605	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 |-
671	669 670	ltsnled	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 |-
672	661	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 |-
673	576	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 |-
674	657	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 |-
675	633	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 |-
676	675	n0nod	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 |-
677	333	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 |-
678	677	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 |-
679		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 |-
680	603	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 |-
681	598	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 |-
682	347	adantr	Could not format ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
683	682	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
684	589	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 |-
685	52 684 350	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 |-
686	685	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 |-
687	683 686	breqtrrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
688	584	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 |-
689	688	n0nod	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 |-
690	322	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 |-
691	689 690 684	pw2ltdivmuls2d	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
692	687 691	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 ) )
693	689 684	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 |-
694	580	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 |-
695	694	n0nod	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 |-
696	693 690 695	ltadds2d	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 ) ) )
697	692 696	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 ) ) )
698	681 697	eqbrtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
699	680 676 698	sltssn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
700	605	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 |-
701		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 )
702	676 700 701	sltssn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { ( g +s 1s ) } < { ( g +s 1s ) } <
703	679 676 699 702	sltsbday	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 |-
704	678 703	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 |-
705	658	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 |-
706	705 395	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 |-
707		n0on	$$⊢g{+}_s{1}_s\in {\mathbb{N}}_{\mathrm{0s}}\to g{+}_s{1}_s\in {On}_s$$
708	675 707	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 |-
709	706 708	onlesd	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 |-
710	704 709	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 |-
711		simpllr	$$⊢\left(\left(\left(\left(\left(d{<}_s\left(j{+}_s{1}_s\right)\wedge g{\le }_{s}c\right)\wedge g{<}_{s}j\right)\wedge \left(g{+}_s{1}_s\right){\le }_{s}j\right)\wedge \left(g{+}_s{1}_s\right){\le }_{s}d\right)\wedge \left(g{+}_s{1}_s\right){<}_{s}d\right)\to \left(g{+}_s{1}_s\right){\le }_{s}j$$
712	711	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 |-
713	672 676 673 710 712	lestrd	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 |-
714	564	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 |-
715		n0sge0	$$⊢l\in {\mathbb{N}}_{\mathrm{0s}}\to 0_s{\le }_{s}l$$
716	714 715	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 |-
717	714	n0nod	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 |-
718	673 717	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 |-
719	716 718	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 |-
720	672 673 674 713 719	lestrd	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 |-
721	720	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 |-
722	671 721	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 |-
723	667 722	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 |-
724		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 |-
725	670 669	lestri3d	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 |-
726	723 724 725	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 |-
727	682	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
728	584	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 |-
729	589	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 |-
730		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 |-
731	412 729 730	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 |-
732		n0ltsp1le	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 |-
733	728 731 732	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 |-
734	727 733	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 |-
735	354	peano2n0sd	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 |-
736	735	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 |-
737	736	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 |-
738	737	n0nod	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 |-
739	731	n0nod	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 |-
740	738 739	lesloed	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 )
741	658	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 |-
742	32 317	ltsnled	$$⊢\phi \to \left(N{<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \neg \left(N{+}_s{1}_s\right){\le }_{s}N\right)$$
743	38 742	mpbid	$$⊢\phi \to \neg \left(N{+}_s{1}_s\right){\le }_{s}N$$
744	741 743	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 |-
745	677	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 |-
746		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 |-
747	580	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 |-
748	747	n0nod	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 |-
749	736	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 |-
750	749	n0nod	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 |-
751	589	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 |-
752	750 751	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 |-
753	748 752	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 |-
754	603	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 |-
755	598	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 |-
756	584	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 |-
757	756	n0nod	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 |-
758	757	ltsp1d	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
759	757 750 751	pw2ltsdiv1d	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 ) )
760	758 759	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 ) )
761	757 751	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 |-
762	761 752 748	ltadds2d	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 ) ) )
763	760 762	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 ) ) )
764	755 763	eqbrtrd	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
765	754 753 764	sltssn	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
766	605	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 |-
767		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 )
768	52 751 350	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 |-
769	768	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 |-
770	767 769	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 )
771	322	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 |-
772	750 771 751	pw2ltdivmuls2d	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 )
773	752 771 748	ltadds2d	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 ) ) )
774	772 773	bitr3d	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 ) ) )
775	770 774	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 ) ) )
776		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 |-
777	775 776	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 ) ) )
778	753 766 777	sltssn	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 ) ) ) } <
779	746 753 765 778	sltsbday	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 |-
780	745 779	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 |-
781	658	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 |-
782	781 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 |-
783	304	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 )
784	783	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 )
785	782 747 749 751 767 784	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 |-
786	780 785	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 |-
787	219 395	onltsd	$$⊢\phi \to \left(N{<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)\right)$$
788	781 787	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 |-
789	788	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 |-
790	317 32	lesnltd	$$⊢\phi \to \left(\left(N{+}_s{1}_s\right){\le }_{s}N\leftrightarrow \neg N{<}_s\left(N{+}_s{1}_s\right)\right)$$
791	781 790	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
792		bdayon	$$⊢\mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{On}$$
793		ontri1	$$⊢\left(\mathrm{bday}\left(N{+}_s{1}_s\right)\in \mathrm{On}\wedge \mathrm{bday}\left(N\right)\in \mathrm{On}\right)\to \left(\mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \neg \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)\right)$$
794	792 8 793	mp2an	$$⊢\mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \neg \mathrm{bday}\left(N\right)\in \mathrm{bday}\left(N{+}_s{1}_s\right)$$
795	794	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 |-
796	789 791 795	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 |-
797	786 796	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 |-
798	797	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 |-
799	744 798	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 )
800		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 |-
801	799 800	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 |-
802	580	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 |-
803	584	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 |-
804		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 |-
805	412 803 804	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 |-
806	805	peano2n0sd	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 |-
807	589	peano2n0sd	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 |-
808	807	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 |-
809		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 |-
810	802	n0nod	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 |-
811	589	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 |-
812	810 811	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 |-
813	812	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 |-
814	52 589 350	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 |-
815	814	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 |-
816	815 810	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 |-
817	584	n0nod	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 |-
818	817	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 |-
819	816 818 811	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 |-
820	598	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 |-
821	813 819 820	3eqtr4rd	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 |-
822	821	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 |-
823		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 |-
824	823 815	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 |-
825	816 824 811	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 |-
826	823	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 |-
827	811	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 |-
828	826 827	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 |-
829	812 828	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 |-
830	825 829	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 |-
831	322	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 |-
832	816 818 831	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 |-
833	832	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 |-
834		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 |-
835	830 833 834	3eqtr4rd	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 |-
836	835	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 |-
837	822 836	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 |-
838	412 811 730	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 |-
839		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 |-
840	838 802 839	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 |-
841		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 |-
842	840 803 841	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 |-
843	842	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 |-
844	843 811	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 |-
845	52	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 |-
846	845 816 818	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 |-
847		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 |-
848	52 811 847	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 |-
849	815 845	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 |-
850	848 849	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 |-
851	850	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 |-
852	845 815 810	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 |-
853	851 852	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 |-
854	853	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 |-
855	846 854	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 |-
856	855	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 |-
857	856	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 |-
858	844 857	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 ) /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 |-
859	809 837 858	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 |-
860		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 |-
861	52 808 860	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 |-
862	861 810	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 |-
863	805	n0nod	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 |-
864	862 863 831	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 |-
865	864	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 |-
866	806	n0nod	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 |-
867	862 866 808	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 |-
868	810 808	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 |-
869	868	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 |-
870	867 869	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 |-
871	859 865 870	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 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 |-
872	831 845 863	ltadds2d	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 )
873	523 872	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 )
874	823	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 |-
875	845 818 831	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 |-
876		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 |-
877	52 876	ax-mp	Could not format ( 2s x.s 1s ) = 2s : No typesetting found for |- ( 2s x.s 1s ) = 2s with typecode |-
878	877	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 |-
879	875 878	eqtrdi	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 |-
880	849 874 879	3eqtr2d	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 |-
881	848 880	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 |-
882	873 881	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 )
883	811	n0nod	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 |-
884	810 883 831	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 |-
885	783	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 )
886	810 883	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 |-
887	658	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 |-
888	887 32	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 |-
889	886 888 831	ltadds1d	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 )
890	885 889	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 )
891	884 890	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 ) )
892		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 |-
893	892	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 |-
894	893	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 |-
895		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 )
896	894 895	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 )
897		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 |-
898	897	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 |-
899	898	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 |-
900	899	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 |-
901	897	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 )
902		oveq2	$$⊢q=i{+}_s{1}_s\to g{+}_{s}q=g{+}_s\left(i{+}_s{1}_s\right)$$
903	902	breq1d	$$⊢q=i{+}_s{1}_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s\left(i{+}_s{1}_s\right)\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
904	900 901 903	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 )
905	535 896 904	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
906	802 806 808 871 882 891 905	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
907	906	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
908	801 907	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
909	740 908	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
910	734 909	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
911	910	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
912	911	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
913	726 912	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
914	913	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
915	652 914	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
916	915	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
917	632 916	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
918	917	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
919	609	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
920	598	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 |-
921	562	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 |-
922		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 |-
923	922	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 |-
924	921 923	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 |-
925	919 920 924	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 ) ) )
926	817	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 |-
927	589	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 |-
928	926 927	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 |-
929	570	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 |-
930	564	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 |-
931	929 930	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 |-
932	580	n0nod	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 |-
933	932	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 |-
934	928 931 933	ltadds2d	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 ) ) )
935	925 934	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 ) )
936	584	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 |-
937	564	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 |-
938	589	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 |-
939		n0subs	$$⊢\left(l\in {\mathbb{N}}_{\mathrm{0s}}\wedge i\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(l{\le }_{s}i\leftrightarrow i{-}_{s}l\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
940	937 938 939	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 |-
941	940	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 |-
942	941	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 |-
943		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 |-
944	412 942 943	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 |-
945	569	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 |-
946		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 |-
947	944 945 946	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 |-
948	589	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 |-
949		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 ) )
950	945	n0nod	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 |-
951	564	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 |-
952	950 951 942	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 |-
953	951	n0nod	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 |-
954	942	n0nod	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 |-
955	953 954	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 |-
956	948	n0nod	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 |-
957		npcans	$$⊢\left(i\in \mathrm{No}\wedge l\in \mathrm{No}\right)\to \left(i{-}_{s}l\right){+}_{s}l=i$$
958	956 953 957	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 |-
959	955 958	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 |-
960	959	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 |-
961	960	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 |-
962	952 961	eqtr2d	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 |-
963	949 962	breqtrrd	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	936	n0nod	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 |-
965	947	n0nod	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 |-
966	964 965 948	pw2ltsdiv1d	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 ) )
967	963 966	mpbird	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
968	682	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
969	563	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
970		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 |-
971	412 951 970	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 |-
972	971	n0nod	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 |-
973	944	n0nod	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 |-
974		nnsgt0	Could not format ( 2s e. NN_s -> 0s 0s
975	410 974	ax-mp	Could not format 0s
976		expsgt0	Could not format ( ( 2s e. No /\ ( i -s l ) e. NN0_s /\ 0s 0s 0s
977	52 975 976	mp3an13	Could not format ( ( i -s l ) e. NN0_s -> 0s 0s
978	942 977	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
979	950 972 973 978	ltmuls2d	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 )
980	969 979	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 )
981		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 |-
982	52 942 951 981	mp3an2i	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 |-
983	958	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 |-
984	982 983	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 |-
985	980 984	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 )
986	967 968 985	3jca	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( h ( h
987	598	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 |-
988	562	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 |-
989		simpllr	Could not format ( ( ( ( ( d g = j ) : No typesetting found for |- ( ( ( ( ( d g = j ) with typecode |-
990	989	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 |-
991	990 962	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 |-
992	988 991	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 |-
993	783	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 )
994	987 992 993	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 )
995		breq1	$$⊢m=h\to \left(m{<}_{s}n\leftrightarrow h{<}_{s}n\right)$$
996		breq1	Could not format ( m = h -> ( m h ( m h
997	995 996	3anbi12d	Could not format ( m = h -> ( ( m ( h ( ( m ( h
998		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 |-
999	998	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 |-
1000	999	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 |-
1001	1000	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 )
1002	997 1001	anbi12d	Could not format ( m = h -> ( ( ( m ( ( h ( ( ( m ( ( h
1003		breq2	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( h h ( h h
1004		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 )
1005	1003 1004	3anbi13d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( ( h ( h ( ( h ( h
1006		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 |-
1007	1006	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 |-
1008	1007	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 |-
1009	1008	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 )
1010	1005 1009	anbi12d	Could not format ( n = ( ( 2s ^su ( i -s l ) ) x.s k ) -> ( ( ( h ( ( h ( ( ( h ( ( h
1011		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 |-
1012	1011	breq2d	Could not format ( o = i -> ( h h ( h h
1013	1011	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 )
1014	1012 1013	3anbi23d	Could not format ( o = i -> ( ( h ( h ( ( h ( h
1015	1011	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 |-
1016	1015	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 |-
1017	1016	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 |-
1018	1011	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 |-
1019	1018	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 |-
1020	1019	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 |-
1021		oveq2	$$⊢o=i\to g{+}_{s}o=g{+}_{s}i$$
1022	1021	breq1d	$$⊢o=i\to \left(\left(g{+}_{s}o\right){<}_{s}N\leftrightarrow \left(g{+}_{s}i\right){<}_{s}N\right)$$
1023	1017 1020 1022	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 )
1024	1014 1023	anbi12d	Could not format ( o = i -> ( ( ( h ( ( h ( ( ( h ( ( h
1025	1002 1010 1024	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
1026	936 947 948 986 994 1025	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
1027	1026	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
1028		n0subs	$$⊢\left(i\in {\mathbb{N}}_{\mathrm{0s}}\wedge l\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(i{\le }_{s}l\leftrightarrow l{-}_{s}i\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
1029	938 937 1028	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 |-
1030	1029	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 |-
1031	1030	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 |-
1032		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 |-
1033	412 1031 1032	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 |-
1034	584	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 |-
1035		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 |-
1036	1033 1034 1035	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 |-
1037	569	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 |-
1038	564	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 |-
1039	1034	n0nod	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 |-
1040	589	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 |-
1041	1039 1040 1031	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 |-
1042	1040	n0nod	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 |-
1043	1031	n0nod	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 |-
1044	1042 1043	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 |-
1045	1044	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 |-
1046	1045	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 |-
1047	1038	n0nod	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 |-
1048		npcans	$$⊢\left(l\in \mathrm{No}\wedge i\in \mathrm{No}\right)\to \left(l{-}_{s}i\right){+}_{s}i=l$$
1049	1047 1042 1048	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 |-
1050	1049	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 |-
1051	1050	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 |-
1052	1041 1046 1051	3eqtrd	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 |-
1053		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 ) )
1054	1052 1053	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 ) )
1055		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 |-
1056	52 1031 1055	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 |-
1057	1056 1039	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 |-
1058	1037	n0nod	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 |-
1059	1057 1058 1038	pw2ltsdiv1d	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 ) )
1060	1054 1059	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 )
1061	682	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s h h
1062	52 1040 350	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 |-
1063		expsgt0	Could not format ( ( 2s e. No /\ ( l -s i ) e. NN0_s /\ 0s 0s 0s
1064	52 975 1063	mp3an13	Could not format ( ( l -s i ) e. NN0_s -> 0s 0s
1065	1031 1064	syl	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
1066	1039 1062 1056 1065	ltmuls2d	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 )
1067	1061 1066	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 )
1068		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 |-
1069	52 1031 1040 1068	mp3an2i	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 |-
1070	1069 1050	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 |-
1071	1067 1070	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 )
1072	563	adantr	Could not format ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s k k
1073	1060 1071 1072	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 )
1074	598	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 |-
1075	1052	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 |-
1076	1074 1075	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 |-
1077	562	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 |-
1078		simpllr	Could not format ( ( ( ( ( d g = j ) : No typesetting found for |- ( ( ( ( ( d g = j ) with typecode |-
1079	1078	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 |-
1080	1079	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 |-
1081	1077 1080	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 |-
1082	1079	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 |-
1083	662	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 )
1084	1082 1083	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 )
1085	1076 1081 1084	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 )
1086		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 )
1087		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 )
1088	1086 1087	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 )
1089		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 |-
1090	1089	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 |-
1091	1090	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 |-
1092	1091	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 )
1093	1088 1092	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 )
1094		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 )
1095		breq1	Could not format ( n = k -> ( n k ( n k
1096	1094 1095	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 )
1097		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 |-
1098	1097	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 |-
1099	1098	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 |-
1100	1099	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 )
1101	1096 1100	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 )
1102		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 |-
1103	1102	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 )
1104	1102	breq2d	Could not format ( o = l -> ( k k ( k k
1105	1103 1104	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 )
1106	1102	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 |-
1107	1106	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 |-
1108	1107	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 |-
1109	1102	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 |-
1110	1109	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 |-
1111	1110	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 |-
1112		oveq2	$$⊢o=l\to g{+}_{s}o=g{+}_{s}l$$
1113	1112	breq1d	$$⊢o=l\to \left(\left(g{+}_{s}o\right){<}_{s}N\leftrightarrow \left(g{+}_{s}l\right){<}_{s}N\right)$$
1114	1108 1111 1113	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 )
1115	1105 1114	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 )
1116	1093 1101 1115	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
1117	1036 1037 1038 1073 1085 1116	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
1118	1117	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
1119	937	n0nod	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 |-
1120	938	n0nod	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 |-
1121		lestric	$$⊢\left(l\in \mathrm{No}\wedge i\in \mathrm{No}\right)\to \left(l{\le }_{s}i\vee i{\le }_{s}l\right)$$
1122	1119 1120 1121	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 |-
1123	1027 1118 1122	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
1124	580	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 |-
1125	1124	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 |-
1126		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 |-
1127		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 |-
1128	412 1126 1127	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 |-
1129	1128	peano2n0sd	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 |-
1130		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 |-
1131	1130	peano2n0sd	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 |-
1132		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 |-
1133	1132	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 |-
1134	1125	n0nod	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 |-
1135	1134 1130	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 |-
1136	1135	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 |-
1137		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 |-
1138	412 1130 1137	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 |-
1139		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 |-
1140	1138 1125 1139	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 |-
1141	1140	n0nod	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 |-
1142	1126	n0nod	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 |-
1143	1141 1142 1130	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 |-
1144		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 |-
1145	1144	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 |-
1146	1136 1143 1145	3eqtr4rd	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 |-
1147	1146	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 |-
1148	1126	peano2n0sd	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 |-
1149	1148	n0nod	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 |-
1150	1141 1149 1130	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 |-
1151	1135	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 |-
1152	1150 1151	eqtr2d	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 |-
1153		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 |-
1154	1153	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 |-
1155	658	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 |-
1156	1155	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 |-
1157	1156 743	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 |-
1158	322	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 |-
1159		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 |-
1160	1159	n0nod	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 |-
1161	1160 1142	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 |-
1162	1158 1161	ltsnled	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 |-
1163	677	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 |-
1164	1163	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 |-
1165	1132	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 |-
1166	1124	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 |-
1167	1166	n0nod	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 |-
1168	1126	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 |-
1169	1168	peano2n0sd	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 |-
1170	1169	n0nod	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 |-
1171	1130	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 |-
1172	1170 1171	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 |-
1173	1167 1172	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 |-
1174	603	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 |-
1175	1174	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 |-
1176	1144	ad2antrl	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 |-
1177	1142	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 |-
1178	1177	ltsp1d	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1179	1177 1170 1171	pw2ltsdiv1d	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 ) )
1180	1177 1171	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 |-
1181	1180 1172 1167	ltadds2d	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 ) ) )
1182	1179 1181	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 ) ) )
1183	1178 1182	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 ) ) )
1184	1176 1183	eqbrtrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s c c
1185	1175 1173 1184	sltssn	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s { c } < { c } <
1186	605	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 |-
1187	1186	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 |-
1188	1142 1158 1160	ltaddsubs2d	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
1189	1188	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 )
1190	1189	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 )
1191	1159	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 |-
1192	1191	n0nod	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 |-
1193	1170 1192 1171	pw2ltsdiv1d	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 ) )
1194	1192 1171	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 |-
1195	1172 1194 1167	ltadds2d	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 ) ) )
1196	1193 1195	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 ) ) )
1197	1190 1196	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 ) ) )
1198	1153	ad2antrl	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 |-
1199	1197 1198	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 ) ) )
1200	1173 1187 1199	sltssn	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 ) ) ) } <
1201	1165 1173 1185 1200	sltsbday	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 |-
1202	1164 1201	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 |-
1203	1155	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 |-
1204	1203 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 |-
1205		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 |-
1206	52 1130 1205	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 |-
1207	1206	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 |-
1208		simprl1	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m m m
1209	1208	ad2antrl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1210		n0ltsp1le	$$⊢\left(m\in {\mathbb{N}}_{\mathrm{0s}}\wedge n\in {\mathbb{N}}_{\mathrm{0s}}\right)\to \left(m{<}_{s}n\leftrightarrow \left(m{+}_s{1}_s\right){\le }_{s}n\right)$$
1211	1168 1191 1210	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 |-
1212	1209 1211	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 |-
1213		simprl3	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m n n
1214	1213	ad2antrl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s n n
1215	1170 1192 1207 1212 1214	leltstrd	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( m +s 1s ) ( m +s 1s )
1216		simprr3	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m ( g +s o ) ( g +s o )
1217	1216	ad2antrl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s ( g +s o ) ( g +s o )
1218	1204 1166 1169 1171 1215 1217	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 |-
1219	1202 1218	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 |-
1220	395 219	onlesd	$$⊢\phi \to \left(\left(N{+}_s{1}_s\right){\le }_{s}N\leftrightarrow \mathrm{bday}\left(N{+}_s{1}_s\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
1221	1203 1220	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 |-
1222	1219 1221	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 |-
1223	1222	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 |-
1224	1162 1223	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 |-
1225	1157 1224	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 |-
1226	1208	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1227		npcans	$$⊢\left(n\in \mathrm{No}\wedge 1_s\in \mathrm{No}\right)\to \left(n{-}_s{1}_s\right){+}_s{1}_s=n$$
1228	1160 322 1227	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 |-
1229	1228	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 |-
1230	1160 1158	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 |-
1231	1142 1230 1158	leadds1d	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 |-
1232	1126 1159 1210	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 |-
1233	1229 1231 1232	3bitr4rd	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 |-
1234	1142 1160 1158	lesubsd	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 |-
1235	1233 1234	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 |-
1236	1226 1235	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 |-
1237	1161 1158	lestri3d	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 |-
1238	1225 1236 1237	mpbir2and	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 |-
1239	1160 1142 1158	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 |-
1240	1238 1239	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 |-
1241	1240	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 |-
1242	1241	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 |-
1243	1242	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 |-
1244	1154 1243	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 |-
1245	1141 1142 1158	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 |-
1246	1245	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 |-
1247	1152 1244 1246	3eqtr4d	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 |-
1248	1247	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 |-
1249	1147 1248	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 |-
1250		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 |-
1251	1140 1126 1250	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 |-
1252	1251	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 |-
1253	1252 1130	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 |-
1254	1133 1249 1253	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 |-
1255	52	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 |-
1256	1255 1141 1142	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 |-
1257		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 |-
1258	52 1130 1257	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 |-
1259	1206 1255	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 |-
1260	1258 1259	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 |-
1261	1260	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 |-
1262	1255 1206 1134	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 |-
1263	1261 1262	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 |-
1264	1263	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 |-
1265	1256 1264	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 |-
1266	1265	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 |-
1267		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 |-
1268	412 1131 1267	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 |-
1269		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 |-
1270	1268 1125 1269	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 |-
1271	1270	n0nod	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 |-
1272	1128	n0nod	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 |-
1273	1271 1272 1158	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 |-
1274	1266 1273	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 |-
1275	1274	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 |-
1276	1254 1275	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 |-
1277	1129	n0nod	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 |-
1278	1271 1277 1131	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 |-
1279	1134 1131	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 |-
1280	1279	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 |-
1281	1276 1278 1280	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 |-
1282		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 |-
1283	412 1148 1282	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 |-
1284	1283	n0nod	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 |-
1285	1268	n0nod	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 |-
1286	1158 1255 1272	ltadds2d	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 )
1287	523 1286	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 )
1288	1255 1142 1158	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 |-
1289	877	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 |-
1290	1288 1289	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 |-
1291	1287 1290	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 )
1292		simprl2	Could not format ( ( ( m e. NN0_s /\ n e. NN0_s /\ o e. NN0_s ) /\ ( ( m m m
1293	1292	adantl	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s m m
1294		n0ltsp1le	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 |-
1295	1126 1138 1294	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 |-
1296	1293 1295	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 |-
1297	975	a1i	Could not format ( ( ( ( ( ( ( ( ph /\ ( w e. No /\ ( ( bday ` w ) = ( bday ` ( N +s 1s ) ) /\ w =/= ( N +s 1s ) ) ) ) /\ 0s 0s 0s
1298	1149 1206 1255 1297	lemuls2d	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 |-
1299	1296 1298	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 |-
1300	1299 1260	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 |-
1301	1277 1284 1285 1291 1300	ltlestrd	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 )
1302	1130	n0nod	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 |-
1303	1134 1302 1158	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 |-
1304	1216	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 )
1305		n0addscl	$$⊢\left(g\in {\mathbb{N}}_{\mathrm{0s}}\wedge o\in {\mathbb{N}}_{\mathrm{0s}}\right)\to g{+}_{s}o\in {\mathbb{N}}_{\mathrm{0s}}$$
1306	1125 1130 1305	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 |-
1307	1306	n0nod	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 |-
1308	1156 32	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 |-
1309	1307 1308 1158	ltadds1d	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 )
1310	1304 1309	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 )
1311	1303 1310	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 ) )
1312		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 |-
1313	1312	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 |-
1314	1313	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 |-
1315		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 )
1316	1314 1315	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 )
1317		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 |-
1318	1317	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 |-
1319	1318	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 |-
1320	1319	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 |-
1321	1317	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 )
1322		oveq2	$$⊢q=o{+}_s{1}_s\to g{+}_{s}q=g{+}_s\left(o{+}_s{1}_s\right)$$
1323	1322	breq1d	$$⊢q=o{+}_s{1}_s\to \left(\left(g{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(g{+}_s\left(o{+}_s{1}_s\right)\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
1324	1320 1321 1323	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 )
1325	535 1316 1324	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
1326	1125 1129 1131 1281 1301 1311 1325	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
1327	1326	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
1328	1327	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
1329	1123 1328	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
1330	1329	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
1331	935 1330	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
1332	1331	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
1333	918 1332	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
1334	627 1333	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
1335	625 1334	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
1336	1335	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
1337	600 1336	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
1338	579 1337	mpdan	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
1339	1338	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
1340	1339	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
1341	229	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 |-
1342	57	a1i	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s\in \mathrm{No}$$
1343	135	3ad2ant1	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to w\in \mathrm{No}$$
1344		simp1r	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{<}_{s}w$$
1345	1343 1344	0elleft	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s\in L\left(w\right)$$
1346	240 1345 189	sltssepcd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{<}_{s}d$$
1347	1342 384 1346	ltlesd	$$⊢\left(\left(\left(\phi \wedge \left(w\in \mathrm{No}\wedge \left(\mathrm{bday}\left(w\right)=\mathrm{bday}\left(N{+}_s{1}_s\right)\wedge w\ne N{+}_s{1}_s\right)\right)\right)\wedge 0_s{<}_{s}w\right)\wedge \left(c\in L\left(w\right)\wedge \forall e\in L\left(w\right)e{\le }_{s}c\right)\wedge \left(d\in R\left(w\right)\wedge \forall f\in R\left(w\right)d{\le }_{s}f\right)\right)\to 0_s{\le }_{s}d$$
1348	1347	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 |-
1349		fveq2	$$⊢z=d\to \mathrm{bday}\left(z\right)=\mathrm{bday}\left(d\right)$$
1350	1349	sseq1d	$$⊢z=d\to \left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\leftrightarrow \mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\right)$$
1351		breq2	$$⊢z=d\to \left(0_s{\le }_{s}z\leftrightarrow 0_s{\le }_{s}d\right)$$
1352	1350 1351	anbi12d	$$⊢z=d\to \left(\left(\mathrm{bday}\left(z\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}z\right)\leftrightarrow \left(\mathrm{bday}\left(d\right)\subseteq \mathrm{bday}\left(N\right)\wedge 0_s{\le }_{s}d\right)\right)$$
1353		eqeq1	$$⊢z=d\to \left(z=N\leftrightarrow d=N\right)$$
1354		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 |-
1355	1354	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
1356	1355	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
1357	1356	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
1358		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 |-
1359	1358	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 |-
1360		oveq1	$$⊢x=j\to x{+}_{s}p=j{+}_{s}p$$
1361	1360	breq1d	$$⊢x=j\to \left(\left(x{+}_{s}p\right){<}_{s}N\leftrightarrow \left(j{+}_{s}p\right){<}_{s}N\right)$$
1362	1359 1361	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
1363	1362	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
1364		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 |-
1365	1364	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 |-
1366	1365	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 |-
1367		breq1	Could not format ( y = k -> ( y k ( y k
1368	1366 1367	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
1369	1368	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
1370		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 |-
1371	1370	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 |-
1372	1371	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 |-
1373	1372	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 |-
1374	1370	breq2d	Could not format ( p = l -> ( k k ( k k
1375		oveq2	$$⊢p=l\to j{+}_{s}p=j{+}_{s}l$$
1376	1375	breq1d	$$⊢p=l\to \left(\left(j{+}_{s}p\right){<}_{s}N\leftrightarrow \left(j{+}_{s}l\right){<}_{s}N\right)$$
1377	1373 1374 1376	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
1378	1377	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
1379	1369 1378	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
1380	1363 1379	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
1381	1357 1380	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
1382	1353 1381	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
1383	1352 1382	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
1384	296 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
1385	1383 1384 385	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
1386	1341 1348 1385	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
1387	561 1340 1386	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
1388	1387	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
1389	1388	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
1390	1389	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
1391	287 1390	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
1392	210 215 1391	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
1393	191 1392	mpdan	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
1394	1393	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
1395	1394	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
1396	186 1395	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
1397	1396	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
1398	180 1397	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
1399	154 175 1398	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
1400	1399	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
1401	150 1400	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
1402	1401	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
1403	144 1402	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
1404	134 138 1403	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
1405	1404	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
1406		addslid	$$⊢0_s\in \mathrm{No}\to 0_s{+}_s{0}_s=0_s$$
1407	57 1406	ax-mp	$$⊢0_s{+}_s{0}_s=0_s$$
1408	1407	eqcomi	$$⊢0_s=0_s{+}_s{0}_s$$
1409		n0p1nns	$$⊢N\in {\mathbb{N}}_{\mathrm{0s}}\to N{+}_s{1}_s\in {\mathbb{N}}_s$$
1410	1 1409	syl	$$⊢\phi \to N{+}_s{1}_s\in {\mathbb{N}}_s$$
1411		nnsgt0	$$⊢N{+}_s{1}_s\in {\mathbb{N}}_s\to 0_s{<}_s\left(N{+}_s{1}_s\right)$$
1412	1410 1411	syl	$$⊢\phi \to 0_s{<}_s\left(N{+}_s{1}_s\right)$$
1413	29 29 29	3pm3.2i	$$⊢\left(0_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge 0_s\in {\mathbb{N}}_{\mathrm{0s}}\wedge 0_s\in {\mathbb{N}}_{\mathrm{0s}}\right)$$
1414		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 |-
1415	1414	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 |-
1416		oveq1	$$⊢a=0_s\to a{+}_{s}q=0_s{+}_{s}q$$
1417	1416	breq1d	$$⊢a=0_s\to \left(\left(a{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow \left(0_s{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\right)$$
1418	1415 1417	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
1419	46	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 |-
1420	1419	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 |-
1421	1420 49	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
1422	60	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 |-
1423	1422	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 |-
1424		oveq2	$$⊢q=0_s\to 0_s{+}_{s}q=0_s{+}_s{0}_s$$
1425	1424 1407	eqtrdi	$$⊢q=0_s\to 0_s{+}_{s}q=0_s$$
1426	1425	breq1d	$$⊢q=0_s\to \left(\left(0_s{+}_{s}q\right){<}_s\left(N{+}_s{1}_s\right)\leftrightarrow 0_s{<}_s\left(N{+}_s{1}_s\right)\right)$$
1427	1423 63 1426	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
1428	1418 1421 1427	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
1429	1413 1428	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
1430	1408 36 1412 1429	mp3an12i	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
1431		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 |-
1432	1431	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
1433	1432	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
1434	1433	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
1435	1430 1434	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
1436	1435	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
1437	1405 1436	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
1438	121 1437	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
1439	1438	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
1440	1439	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
1441	1440	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
1442	1441	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
1443	1442	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
1444	118 1443	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
1445	1444	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
1446	1445	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
1447	1446	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
1448	117 1447	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
1449	116 1448	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
1450	14 1449	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
1451	6 1450	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
1452	1451	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
1453	1452	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