Theorem sleadd1

Description: Addition to both sides of surreal less-than or equal. Theorem 5 of Conway p. 18. (Contributed by Scott Fenton, 21-Jan-2025)

	Ref	Expression
Assertion	sleadd1	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A <_s B <-> ( A +s C ) <_s ( B +s C ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		oveq1	Could not format ( x = xO -> ( x +s z ) = ( xO +s z ) ) : No typesetting found for |- ( x = xO -> ( x +s z ) = ( xO +s z ) ) with typecode |-
2	1	breq2d	Could not format ( x = xO -> ( ( y +s z ) ( y +s z ) ( ( y +s z ) ( y +s z )
3		breq2	Could not format ( x = xO -> ( y y ( y y
4	2 3	imbi12d	Could not format ( x = xO -> ( ( ( y +s z ) y ( ( y +s z ) y ( ( ( y +s z ) y ( ( y +s z ) y
5		oveq1	Could not format ( y = yO -> ( y +s z ) = ( yO +s z ) ) : No typesetting found for |- ( y = yO -> ( y +s z ) = ( yO +s z ) ) with typecode |-
6	5	breq1d	Could not format ( y = yO -> ( ( y +s z ) ( yO +s z ) ( ( y +s z ) ( yO +s z )
7		breq1	Could not format ( y = yO -> ( y yO ( y yO
8	6 7	imbi12d	Could not format ( y = yO -> ( ( ( y +s z ) y ( ( yO +s z ) yO ( ( ( y +s z ) y ( ( yO +s z ) yO
9		oveq2	Could not format ( z = zO -> ( yO +s z ) = ( yO +s zO ) ) : No typesetting found for |- ( z = zO -> ( yO +s z ) = ( yO +s zO ) ) with typecode |-
10		oveq2	Could not format ( z = zO -> ( xO +s z ) = ( xO +s zO ) ) : No typesetting found for |- ( z = zO -> ( xO +s z ) = ( xO +s zO ) ) with typecode |-
11	9 10	breq12d	Could not format ( z = zO -> ( ( yO +s z ) ( yO +s zO ) ( ( yO +s z ) ( yO +s zO )
12	11	imbi1d	Could not format ( z = zO -> ( ( ( yO +s z ) yO ( ( yO +s zO ) yO ( ( ( yO +s z ) yO ( ( yO +s zO ) yO
13		oveq1	Could not format ( x = xO -> ( x +s zO ) = ( xO +s zO ) ) : No typesetting found for |- ( x = xO -> ( x +s zO ) = ( xO +s zO ) ) with typecode |-
14	13	breq2d	Could not format ( x = xO -> ( ( yO +s zO ) ( yO +s zO ) ( ( yO +s zO ) ( yO +s zO )
15		breq2	Could not format ( x = xO -> ( yO yO ( yO yO
16	14 15	imbi12d	Could not format ( x = xO -> ( ( ( yO +s zO ) yO ( ( yO +s zO ) yO ( ( ( yO +s zO ) yO ( ( yO +s zO ) yO
17		oveq1	Could not format ( y = yO -> ( y +s zO ) = ( yO +s zO ) ) : No typesetting found for |- ( y = yO -> ( y +s zO ) = ( yO +s zO ) ) with typecode |-
18	17	breq1d	Could not format ( y = yO -> ( ( y +s zO ) ( yO +s zO ) ( ( y +s zO ) ( yO +s zO )
19		breq1	Could not format ( y = yO -> ( y yO ( y yO
20	18 19	imbi12d	Could not format ( y = yO -> ( ( ( y +s zO ) y ( ( yO +s zO ) yO ( ( ( y +s zO ) y ( ( yO +s zO ) yO
21	17	breq1d	Could not format ( y = yO -> ( ( y +s zO ) ( yO +s zO ) ( ( y +s zO ) ( yO +s zO )
22	21 7	imbi12d	Could not format ( y = yO -> ( ( ( y +s zO ) y ( ( yO +s zO ) yO ( ( ( y +s zO ) y ( ( yO +s zO ) yO
23		oveq2	Could not format ( z = zO -> ( x +s z ) = ( x +s zO ) ) : No typesetting found for |- ( z = zO -> ( x +s z ) = ( x +s zO ) ) with typecode |-
24	9 23	breq12d	Could not format ( z = zO -> ( ( yO +s z ) ( yO +s zO ) ( ( yO +s z ) ( yO +s zO )
25	24	imbi1d	Could not format ( z = zO -> ( ( ( yO +s z ) yO ( ( yO +s zO ) yO ( ( ( yO +s z ) yO ( ( yO +s zO ) yO
26		oveq1	Could not format ( x = A -> ( x +s z ) = ( A +s z ) ) : No typesetting found for |- ( x = A -> ( x +s z ) = ( A +s z ) ) with typecode |-
27	26	breq2d	Could not format ( x = A -> ( ( y +s z ) ( y +s z ) ( ( y +s z ) ( y +s z )
28		breq2	$$⊢x=A\to \left(y{<}_{s}x\leftrightarrow y{<}_{s}A\right)$$
29	27 28	imbi12d	Could not format ( x = A -> ( ( ( y +s z ) y ( ( y +s z ) y ( ( ( y +s z ) y ( ( y +s z ) y
30		oveq1	Could not format ( y = B -> ( y +s z ) = ( B +s z ) ) : No typesetting found for |- ( y = B -> ( y +s z ) = ( B +s z ) ) with typecode |-
31	30	breq1d	Could not format ( y = B -> ( ( y +s z ) ( B +s z ) ( ( y +s z ) ( B +s z )
32		breq1	$$⊢y=B\to \left(y{<}_{s}A\leftrightarrow B{<}_{s}A\right)$$
33	31 32	imbi12d	Could not format ( y = B -> ( ( ( y +s z ) y ( ( B +s z ) B ( ( ( y +s z ) y ( ( B +s z ) B
34		oveq2	Could not format ( z = C -> ( B +s z ) = ( B +s C ) ) : No typesetting found for |- ( z = C -> ( B +s z ) = ( B +s C ) ) with typecode |-
35		oveq2	Could not format ( z = C -> ( A +s z ) = ( A +s C ) ) : No typesetting found for |- ( z = C -> ( A +s z ) = ( A +s C ) ) with typecode |-
36	34 35	breq12d	Could not format ( z = C -> ( ( B +s z ) ( B +s C ) ( ( B +s z ) ( B +s C )
37	36	imbi1d	Could not format ( z = C -> ( ( ( B +s z ) B ( ( B +s C ) B ( ( ( B +s z ) B ( ( B +s C ) B
38		simp2	$$⊢\left(x\in \mathrm{No}\wedge y\in \mathrm{No}\wedge z\in \mathrm{No}\right)\to y\in \mathrm{No}$$
39		simp3	$$⊢\left(x\in \mathrm{No}\wedge y\in \mathrm{No}\wedge z\in \mathrm{No}\right)\to z\in \mathrm{No}$$
40	38 39	addscut	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( ( y +s z ) e. No /\ ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( ( y +s z ) e. No /\ ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
41		simp2	Could not format ( ( ( y +s z ) e. No /\ ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
42	40 41	syl	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
43	40	simp3d	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> { ( y +s z ) } < { ( y +s z ) } <
44		ovex	Could not format ( y +s z ) e. _V : No typesetting found for |- ( y +s z ) e. _V with typecode |-
45	44	snnz	Could not format { ( y +s z ) } =/= (/) : No typesetting found for |- { ( y +s z ) } =/= (/) with typecode |-
46		sslttr	Could not format ( ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
47	45 46	mp3an3	Could not format ( ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
48	42 43 47	syl2anc	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) <
49		simp1	$$⊢\left(x\in \mathrm{No}\wedge y\in \mathrm{No}\wedge z\in \mathrm{No}\right)\to x\in \mathrm{No}$$
50	49 39	addscut	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( ( x +s z ) e. No /\ ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( ( x +s z ) e. No /\ ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
51		simp2	Could not format ( ( ( x +s z ) e. No /\ ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
52	50 51	syl	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
53	50	simp3d	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> { ( x +s z ) } < { ( x +s z ) } <
54		ovex	Could not format ( x +s z ) e. _V : No typesetting found for |- ( x +s z ) e. _V with typecode |-
55	54	snnz	Could not format { ( x +s z ) } =/= (/) : No typesetting found for |- { ( x +s z ) } =/= (/) with typecode |-
56		sslttr	Could not format ( ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
57	55 56	mp3an3	Could not format ( ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
58	52 53 57	syl2anc	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) < ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) <
59		addsval2	Could not format ( ( y e. No /\ z e. No ) -> ( y +s z ) = ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) |s ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) ) ) : No typesetting found for |- ( ( y e. No /\ z e. No ) -> ( y +s z ) = ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) |s ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) ) ) with typecode |-
60	59	3adant1	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( y +s z ) = ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) |s ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) ) ) : No typesetting found for |- ( ( x e. No /\ y e. No /\ z e. No ) -> ( y +s z ) = ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) |s ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) ) ) with typecode |-
61		addsval2	Could not format ( ( x e. No /\ z e. No ) -> ( x +s z ) = ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) |s ( { c | E. xR e. ( _Right ` x ) c = ( xR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( x +s zR ) } ) ) ) : No typesetting found for |- ( ( x e. No /\ z e. No ) -> ( x +s z ) = ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) |s ( { c | E. xR e. ( _Right ` x ) c = ( xR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( x +s zR ) } ) ) ) with typecode |-
62	61	3adant2	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( x +s z ) = ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) |s ( { c | E. xR e. ( _Right ` x ) c = ( xR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( x +s zR ) } ) ) ) : No typesetting found for |- ( ( x e. No /\ y e. No /\ z e. No ) -> ( x +s z ) = ( ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) |s ( { c | E. xR e. ( _Right ` x ) c = ( xR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( x +s zR ) } ) ) ) with typecode |-
63		sltrec	Could not format ( ( ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) : No typesetting found for |- ( ( ( ( { a | E. yL e. ( _Left ` y ) a = ( yL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( y +s zL ) } ) < ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) with typecode |-
64	48 58 60 62 63	syl22anc	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) : No typesetting found for |- ( ( x e. No /\ y e. No /\ z e. No ) -> ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) with typecode |-
65	64	adantr	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) : No typesetting found for |- ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) ) ) with typecode |-
66		rexun	Could not format ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p <-> ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p \/ E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p <-> ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p \/ E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p ) ) with typecode |-
67		eqeq1	Could not format ( a = p -> ( a = ( xL +s z ) <-> p = ( xL +s z ) ) ) : No typesetting found for |- ( a = p -> ( a = ( xL +s z ) <-> p = ( xL +s z ) ) ) with typecode |-
68	67	rexbidv	Could not format ( a = p -> ( E. xL e. ( _Left ` x ) a = ( xL +s z ) <-> E. xL e. ( _Left ` x ) p = ( xL +s z ) ) ) : No typesetting found for |- ( a = p -> ( E. xL e. ( _Left ` x ) a = ( xL +s z ) <-> E. xL e. ( _Left ` x ) p = ( xL +s z ) ) ) with typecode |-
69	68	rexab	Could not format ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) with typecode |-
70		rexcom4	Could not format ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) with typecode |-
71		r19.41v	Could not format ( E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) with typecode |-
72	71	exbii	Could not format ( E. p E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. p E. xL e. ( _Left ` x ) ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) with typecode |-
73	70 72	bitri	Could not format ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) ) with typecode |-
74		ovex	Could not format ( xL +s z ) e. _V : No typesetting found for |- ( xL +s z ) e. _V with typecode |-
75		breq2	Could not format ( p = ( xL +s z ) -> ( ( y +s z ) <_s p <-> ( y +s z ) <_s ( xL +s z ) ) ) : No typesetting found for |- ( p = ( xL +s z ) -> ( ( y +s z ) <_s p <-> ( y +s z ) <_s ( xL +s z ) ) ) with typecode |-
76	74 75	ceqsexv	Could not format ( E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> ( y +s z ) <_s ( xL +s z ) ) : No typesetting found for |- ( E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> ( y +s z ) <_s ( xL +s z ) ) with typecode |-
77	76	rexbii	Could not format ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) : No typesetting found for |- ( E. xL e. ( _Left ` x ) E. p ( p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) with typecode |-
78	73 77	bitr3i	Could not format ( E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) : No typesetting found for |- ( E. p ( E. xL e. ( _Left ` x ) p = ( xL +s z ) /\ ( y +s z ) <_s p ) <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) with typecode |-
79	69 78	bitri	Could not format ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) : No typesetting found for |- ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p <-> E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) ) with typecode |-
80		eqeq1	Could not format ( b = p -> ( b = ( x +s zL ) <-> p = ( x +s zL ) ) ) : No typesetting found for |- ( b = p -> ( b = ( x +s zL ) <-> p = ( x +s zL ) ) ) with typecode |-
81	80	rexbidv	Could not format ( b = p -> ( E. zL e. ( _Left ` z ) b = ( x +s zL ) <-> E. zL e. ( _Left ` z ) p = ( x +s zL ) ) ) : No typesetting found for |- ( b = p -> ( E. zL e. ( _Left ` z ) b = ( x +s zL ) <-> E. zL e. ( _Left ` z ) p = ( x +s zL ) ) ) with typecode |-
82	81	rexab	Could not format ( E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) with typecode |-
83		rexcom4	Could not format ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) with typecode |-
84		r19.41v	Could not format ( E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) with typecode |-
85	84	exbii	Could not format ( E. p E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. p E. zL e. ( _Left ` z ) ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) with typecode |-
86	83 85	bitri	Could not format ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) : No typesetting found for |- ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) ) with typecode |-
87		ovex	Could not format ( x +s zL ) e. _V : No typesetting found for |- ( x +s zL ) e. _V with typecode |-
88		breq2	Could not format ( p = ( x +s zL ) -> ( ( y +s z ) <_s p <-> ( y +s z ) <_s ( x +s zL ) ) ) : No typesetting found for |- ( p = ( x +s zL ) -> ( ( y +s z ) <_s p <-> ( y +s z ) <_s ( x +s zL ) ) ) with typecode |-
89	87 88	ceqsexv	Could not format ( E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> ( y +s z ) <_s ( x +s zL ) ) : No typesetting found for |- ( E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> ( y +s z ) <_s ( x +s zL ) ) with typecode |-
90	89	rexbii	Could not format ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) : No typesetting found for |- ( E. zL e. ( _Left ` z ) E. p ( p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) with typecode |-
91	86 90	bitr3i	Could not format ( E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) : No typesetting found for |- ( E. p ( E. zL e. ( _Left ` z ) p = ( x +s zL ) /\ ( y +s z ) <_s p ) <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) with typecode |-
92	82 91	bitri	Could not format ( E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) : No typesetting found for |- ( E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p <-> E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) with typecode |-
93	79 92	orbi12i	Could not format ( ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p \/ E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p ) <-> ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) ) : No typesetting found for |- ( ( E. p e. { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } ( y +s z ) <_s p \/ E. p e. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ( y +s z ) <_s p ) <-> ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) ) with typecode |-
94	66 93	bitri	Could not format ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p <-> ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) ) : No typesetting found for |- ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p <-> ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) ) with typecode |-
95		simpll2	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) with typecode |-
96		leftssno	Could not format ( _Left ` x ) C_ No : No typesetting found for |- ( _Left ` x ) C_ No with typecode |-
97	96	sseli	Could not format ( xL e. ( _Left ` x ) -> xL e. No ) : No typesetting found for |- ( xL e. ( _Left ` x ) -> xL e. No ) with typecode |-
98	97	adantr	Could not format ( ( xL e. ( _Left ` x ) /\ ( y +s z ) <_s ( xL +s z ) ) -> xL e. No ) : No typesetting found for |- ( ( xL e. ( _Left ` x ) /\ ( y +s z ) <_s ( xL +s z ) ) -> xL e. No ) with typecode |-
99	98	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y xL e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y xL e. No ) with typecode |-
100		simpll1	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) with typecode |-
101		simprr	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) <_s ( xL +s z ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) <_s ( xL +s z ) ) with typecode |-
102		simpll3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) with typecode |-
103		sleadd1im	Could not format ( ( y e. No /\ xL e. No /\ z e. No ) -> ( ( y +s z ) <_s ( xL +s z ) -> y <_s xL ) ) : No typesetting found for |- ( ( y e. No /\ xL e. No /\ z e. No ) -> ( ( y +s z ) <_s ( xL +s z ) -> y <_s xL ) ) with typecode |-
104	95 99 102 103	syl3anc	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) <_s ( xL +s z ) -> y <_s xL ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) <_s ( xL +s z ) -> y <_s xL ) ) with typecode |-
105	101 104	mpd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y <_s xL ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y <_s xL ) with typecode |-
106		leftval	Could not format ( _Left ` x ) = { xL e. ( _Old ` ( bday ` x ) ) | xL
107	106	reqabi	Could not format ( xL e. ( _Left ` x ) <-> ( xL e. ( _Old ` ( bday ` x ) ) /\ xL ( xL e. ( _Old ` ( bday ` x ) ) /\ xL
108	107	simprbi	Could not format ( xL e. ( _Left ` x ) -> xL xL
109	108	adantr	Could not format ( ( xL e. ( _Left ` x ) /\ ( y +s z ) <_s ( xL +s z ) ) -> xL xL
110	109	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y xL yO yO y y yO yO y xL
111	95 99 100 105 110	slelttrd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y yO yO y y yO yO y y
112	111	rexlimdvaa	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) -> y yO yO y y yO yO y ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) -> y
113		simpll2	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) with typecode |-
114		leftssno	Could not format ( _Left ` z ) C_ No : No typesetting found for |- ( _Left ` z ) C_ No with typecode |-
115	114	sseli	Could not format ( zL e. ( _Left ` z ) -> zL e. No ) : No typesetting found for |- ( zL e. ( _Left ` z ) -> zL e. No ) with typecode |-
116	115	adantr	Could not format ( ( zL e. ( _Left ` z ) /\ ( y +s z ) <_s ( x +s zL ) ) -> zL e. No ) : No typesetting found for |- ( ( zL e. ( _Left ` z ) /\ ( y +s z ) <_s ( x +s zL ) ) -> zL e. No ) with typecode |-
117	116	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. No ) with typecode |-
118	113 117	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zL ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zL ) e. No ) with typecode |-
119		simpll3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) with typecode |-
120	113 119	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) e. No ) with typecode |-
121		simpll1	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) with typecode |-
122	121 117	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s zL ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s zL ) e. No ) with typecode |-
123		leftval	Could not format ( _Left ` z ) = { zL e. ( _Old ` ( bday ` z ) ) | zL
124	123	reqabi	Could not format ( zL e. ( _Left ` z ) <-> ( zL e. ( _Old ` ( bday ` z ) ) /\ zL ( zL e. ( _Old ` ( bday ` z ) ) /\ zL
125	124	simprbi	Could not format ( zL e. ( _Left ` z ) -> zL zL
126	125	adantr	Could not format ( ( zL e. ( _Left ` z ) /\ ( y +s z ) <_s ( x +s zL ) ) -> zL zL
127	126	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL yO yO y y yO yO y zL
128		sltadd2im	Could not format ( ( zL e. No /\ z e. No /\ y e. No ) -> ( zL ( y +s zL ) ( zL ( y +s zL )
129	117 119 113 128	syl3anc	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( zL ( y +s zL ) yO yO y y yO yO y ( zL ( y +s zL )
130	127 129	mpd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zL ) yO yO y y yO yO y ( y +s zL )
131		simprr	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) <_s ( x +s zL ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s z ) <_s ( x +s zL ) ) with typecode |-
132	118 120 122 130 131	sltletrd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zL ) yO yO y y yO yO y ( y +s zL )
133		oveq2	Could not format ( zO = zL -> ( y +s zO ) = ( y +s zL ) ) : No typesetting found for |- ( zO = zL -> ( y +s zO ) = ( y +s zL ) ) with typecode |-
134		oveq2	Could not format ( zO = zL -> ( x +s zO ) = ( x +s zL ) ) : No typesetting found for |- ( zO = zL -> ( x +s zO ) = ( x +s zL ) ) with typecode |-
135	133 134	breq12d	Could not format ( zO = zL -> ( ( y +s zO ) ( y +s zL ) ( ( y +s zO ) ( y +s zL )
136	135	imbi1d	Could not format ( zO = zL -> ( ( ( y +s zO ) y ( ( y +s zL ) y ( ( ( y +s zO ) y ( ( y +s zL ) y
137		simplr3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( y +s zO ) y yO yO y y yO yO y A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( y +s zO ) y
138		simprl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. ( _Left ` z ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. ( _Left ` z ) ) with typecode |-
139		elun1	Could not format ( zL e. ( _Left ` z ) -> zL e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) : No typesetting found for |- ( zL e. ( _Left ` z ) -> zL e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) with typecode |-
140	138 139	syl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zL e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) with typecode |-
141	136 137 140	rspcdva	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s zL ) y yO yO y y yO yO y ( ( y +s zL ) y
142	132 141	mpd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y yO yO y y yO yO y y
143	142	rexlimdvaa	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) -> y yO yO y y yO yO y ( E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) -> y
144	112 143	jaod	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) -> y yO yO y y yO yO y ( ( E. xL e. ( _Left ` x ) ( y +s z ) <_s ( xL +s z ) \/ E. zL e. ( _Left ` z ) ( y +s z ) <_s ( x +s zL ) ) -> y
145	94 144	biimtrid	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p -> y yO yO y y yO yO y ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p -> y
146		rexun	Could not format ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) <-> ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) \/ E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) <-> ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) \/ E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) ) ) with typecode |-
147		eqeq1	Could not format ( c = q -> ( c = ( yR +s z ) <-> q = ( yR +s z ) ) ) : No typesetting found for |- ( c = q -> ( c = ( yR +s z ) <-> q = ( yR +s z ) ) ) with typecode |-
148	147	rexbidv	Could not format ( c = q -> ( E. yR e. ( _Right ` y ) c = ( yR +s z ) <-> E. yR e. ( _Right ` y ) q = ( yR +s z ) ) ) : No typesetting found for |- ( c = q -> ( E. yR e. ( _Right ` y ) c = ( yR +s z ) <-> E. yR e. ( _Right ` y ) q = ( yR +s z ) ) ) with typecode |-
149	148	rexab	Could not format ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) with typecode |-
150		rexcom4	Could not format ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) with typecode |-
151		r19.41v	Could not format ( E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) with typecode |-
152	151	exbii	Could not format ( E. q E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q E. yR e. ( _Right ` y ) ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) with typecode |-
153	150 152	bitri	Could not format ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) ) with typecode |-
154		ovex	Could not format ( yR +s z ) e. _V : No typesetting found for |- ( yR +s z ) e. _V with typecode |-
155		breq1	Could not format ( q = ( yR +s z ) -> ( q <_s ( x +s z ) <-> ( yR +s z ) <_s ( x +s z ) ) ) : No typesetting found for |- ( q = ( yR +s z ) -> ( q <_s ( x +s z ) <-> ( yR +s z ) <_s ( x +s z ) ) ) with typecode |-
156	154 155	ceqsexv	Could not format ( E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> ( yR +s z ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> ( yR +s z ) <_s ( x +s z ) ) with typecode |-
157	156	rexbii	Could not format ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) : No typesetting found for |- ( E. yR e. ( _Right ` y ) E. q ( q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) with typecode |-
158	153 157	bitr3i	Could not format ( E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q ( E. yR e. ( _Right ` y ) q = ( yR +s z ) /\ q <_s ( x +s z ) ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) with typecode |-
159	149 158	bitri	Could not format ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) <-> E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) ) with typecode |-
160		eqeq1	Could not format ( d = q -> ( d = ( y +s zR ) <-> q = ( y +s zR ) ) ) : No typesetting found for |- ( d = q -> ( d = ( y +s zR ) <-> q = ( y +s zR ) ) ) with typecode |-
161	160	rexbidv	Could not format ( d = q -> ( E. zR e. ( _Right ` z ) d = ( y +s zR ) <-> E. zR e. ( _Right ` z ) q = ( y +s zR ) ) ) : No typesetting found for |- ( d = q -> ( E. zR e. ( _Right ` z ) d = ( y +s zR ) <-> E. zR e. ( _Right ` z ) q = ( y +s zR ) ) ) with typecode |-
162	161	rexab	Could not format ( E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) with typecode |-
163		rexcom4	Could not format ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) with typecode |-
164		r19.41v	Could not format ( E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) with typecode |-
165	164	exbii	Could not format ( E. q E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q E. zR e. ( _Right ` z ) ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) with typecode |-
166	163 165	bitri	Could not format ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) : No typesetting found for |- ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) ) with typecode |-
167		ovex	Could not format ( y +s zR ) e. _V : No typesetting found for |- ( y +s zR ) e. _V with typecode |-
168		breq1	Could not format ( q = ( y +s zR ) -> ( q <_s ( x +s z ) <-> ( y +s zR ) <_s ( x +s z ) ) ) : No typesetting found for |- ( q = ( y +s zR ) -> ( q <_s ( x +s z ) <-> ( y +s zR ) <_s ( x +s z ) ) ) with typecode |-
169	167 168	ceqsexv	Could not format ( E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> ( y +s zR ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> ( y +s zR ) <_s ( x +s z ) ) with typecode |-
170	169	rexbii	Could not format ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) : No typesetting found for |- ( E. zR e. ( _Right ` z ) E. q ( q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) with typecode |-
171	166 170	bitr3i	Could not format ( E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q ( E. zR e. ( _Right ` z ) q = ( y +s zR ) /\ q <_s ( x +s z ) ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) with typecode |-
172	162 171	bitri	Could not format ( E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) : No typesetting found for |- ( E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) <-> E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) with typecode |-
173	159 172	orbi12i	Could not format ( ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) \/ E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) ) <-> ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) ) : No typesetting found for |- ( ( E. q e. { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } q <_s ( x +s z ) \/ E. q e. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } q <_s ( x +s z ) ) <-> ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) ) with typecode |-
174	146 173	bitri	Could not format ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) <-> ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) ) : No typesetting found for |- ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) <-> ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) ) with typecode |-
175		simpll2	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) with typecode |-
176		rightssno	Could not format ( _Right ` y ) C_ No : No typesetting found for |- ( _Right ` y ) C_ No with typecode |-
177	176	sseli	Could not format ( yR e. ( _Right ` y ) -> yR e. No ) : No typesetting found for |- ( yR e. ( _Right ` y ) -> yR e. No ) with typecode |-
178	177	adantr	Could not format ( ( yR e. ( _Right ` y ) /\ ( yR +s z ) <_s ( x +s z ) ) -> yR e. No ) : No typesetting found for |- ( ( yR e. ( _Right ` y ) /\ ( yR +s z ) <_s ( x +s z ) ) -> yR e. No ) with typecode |-
179	178	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y yR e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y yR e. No ) with typecode |-
180		simpll1	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) with typecode |-
181		rightval	Could not format ( _Right ` y ) = { yR e. ( _Old ` ( bday ` y ) ) | y
182	181	reqabi	Could not format ( yR e. ( _Right ` y ) <-> ( yR e. ( _Old ` ( bday ` y ) ) /\ y ( yR e. ( _Old ` ( bday ` y ) ) /\ y
183	182	simprbi	Could not format ( yR e. ( _Right ` y ) -> y y
184	183	adantr	Could not format ( ( yR e. ( _Right ` y ) /\ ( yR +s z ) <_s ( x +s z ) ) -> y y
185	184	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y yO yO y y yO yO y y
186		simprr	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( yR +s z ) <_s ( x +s z ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( yR +s z ) <_s ( x +s z ) ) with typecode |-
187		simpll3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) with typecode |-
188		sleadd1im	Could not format ( ( yR e. No /\ x e. No /\ z e. No ) -> ( ( yR +s z ) <_s ( x +s z ) -> yR <_s x ) ) : No typesetting found for |- ( ( yR e. No /\ x e. No /\ z e. No ) -> ( ( yR +s z ) <_s ( x +s z ) -> yR <_s x ) ) with typecode |-
189	179 180 187 188	syl3anc	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( yR +s z ) <_s ( x +s z ) -> yR <_s x ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( yR +s z ) <_s ( x +s z ) -> yR <_s x ) ) with typecode |-
190	186 189	mpd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y yR <_s x ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y yR <_s x ) with typecode |-
191	175 179 180 185 190	sltletrd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y yO yO y y yO yO y y
192	191	rexlimdvaa	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) -> y yO yO y y yO yO y ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) -> y
193		simpll2	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y e. No ) with typecode |-
194		rightssno	Could not format ( _Right ` z ) C_ No : No typesetting found for |- ( _Right ` z ) C_ No with typecode |-
195	194	sseli	Could not format ( zR e. ( _Right ` z ) -> zR e. No ) : No typesetting found for |- ( zR e. ( _Right ` z ) -> zR e. No ) with typecode |-
196	195	adantr	Could not format ( ( zR e. ( _Right ` z ) /\ ( y +s zR ) <_s ( x +s z ) ) -> zR e. No ) : No typesetting found for |- ( ( zR e. ( _Right ` z ) /\ ( y +s zR ) <_s ( x +s z ) ) -> zR e. No ) with typecode |-
197	196	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. No ) with typecode |-
198	193 197	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zR ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zR ) e. No ) with typecode |-
199		simpll1	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y x e. No ) with typecode |-
200		simpll3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z e. No ) with typecode |-
201	199 200	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s z ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s z ) e. No ) with typecode |-
202	199 197	addscld	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s zR ) e. No ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s zR ) e. No ) with typecode |-
203		simprr	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zR ) <_s ( x +s z ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zR ) <_s ( x +s z ) ) with typecode |-
204	200 197 199	3jca	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( z e. No /\ zR e. No /\ x e. No ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( z e. No /\ zR e. No /\ x e. No ) ) with typecode |-
205		rightval	Could not format ( _Right ` z ) = { zR e. ( _Old ` ( bday ` z ) ) | z
206	205	reqabi	Could not format ( zR e. ( _Right ` z ) <-> ( zR e. ( _Old ` ( bday ` z ) ) /\ z ( zR e. ( _Old ` ( bday ` z ) ) /\ z
207	206	simprbi	Could not format ( zR e. ( _Right ` z ) -> z z
208	207	adantr	Could not format ( ( zR e. ( _Right ` z ) /\ ( y +s zR ) <_s ( x +s z ) ) -> z z
209	208	adantl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y z yO yO y y yO yO y z
210		sltadd2im	Could not format ( ( z e. No /\ zR e. No /\ x e. No ) -> ( z ( x +s z ) ( z ( x +s z )
211	204 209 210	sylc	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( x +s z ) yO yO y y yO yO y ( x +s z )
212	198 201 202 203 211	slelttrd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( y +s zR ) yO yO y y yO yO y ( y +s zR )
213		oveq2	Could not format ( zO = zR -> ( y +s zO ) = ( y +s zR ) ) : No typesetting found for |- ( zO = zR -> ( y +s zO ) = ( y +s zR ) ) with typecode |-
214		oveq2	Could not format ( zO = zR -> ( x +s zO ) = ( x +s zR ) ) : No typesetting found for |- ( zO = zR -> ( x +s zO ) = ( x +s zR ) ) with typecode |-
215	213 214	breq12d	Could not format ( zO = zR -> ( ( y +s zO ) ( y +s zR ) ( ( y +s zO ) ( y +s zR )
216	215	imbi1d	Could not format ( zO = zR -> ( ( ( y +s zO ) y ( ( y +s zR ) y ( ( ( y +s zO ) y ( ( y +s zR ) y
217		simplr3	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( y +s zO ) y yO yO y y yO yO y A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( y +s zO ) y
218		simprl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. ( _Right ` z ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. ( _Right ` z ) ) with typecode |-
219		elun2	Could not format ( zR e. ( _Right ` z ) -> zR e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) : No typesetting found for |- ( zR e. ( _Right ` z ) -> zR e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) with typecode |-
220	218 219	syl	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) : No typesetting found for |- ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y zR e. ( ( _Left ` z ) u. ( _Right ` z ) ) ) with typecode |-
221	216 217 220	rspcdva	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s zR ) y yO yO y y yO yO y ( ( y +s zR ) y
222	212 221	mpd	Could not format ( ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y y yO yO y y yO yO y y
223	222	rexlimdvaa	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) -> y yO yO y y yO yO y ( E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) -> y
224	192 223	jaod	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) -> y yO yO y y yO yO y ( ( E. yR e. ( _Right ` y ) ( yR +s z ) <_s ( x +s z ) \/ E. zR e. ( _Right ` z ) ( y +s zR ) <_s ( x +s z ) ) -> y
225	174 224	biimtrid	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) -> y yO yO y y yO yO y ( E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) -> y
226	145 225	jaod	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) -> y yO yO y y yO yO y ( ( E. p e. ( { a | E. xL e. ( _Left ` x ) a = ( xL +s z ) } u. { b | E. zL e. ( _Left ` z ) b = ( x +s zL ) } ) ( y +s z ) <_s p \/ E. q e. ( { c | E. yR e. ( _Right ` y ) c = ( yR +s z ) } u. { d | E. zR e. ( _Right ` z ) d = ( y +s zR ) } ) q <_s ( x +s z ) ) -> y
227	65 226	sylbid	Could not format ( ( ( x e. No /\ y e. No /\ z e. No ) /\ ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) y yO yO y y yO yO y ( ( y +s z ) y
228	227	ex	Could not format ( ( x e. No /\ y e. No /\ z e. No ) -> ( ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) y ( ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) A. yO e. ( ( _Left ` y ) u. ( _Right ` y ) ) A. zO e. ( ( _Left ` z ) u. ( _Right ` z ) ) ( ( yO +s zO ) yO yO y y yO yO y ( ( y +s z ) y
229	4 8 12 16 20 22 25 29 33 37 228	no3inds	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( B +s C ) B ( ( B +s C ) B
230		addscl	Could not format ( ( B e. No /\ C e. No ) -> ( B +s C ) e. No ) : No typesetting found for |- ( ( B e. No /\ C e. No ) -> ( B +s C ) e. No ) with typecode |-
231	230	3adant1	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( B +s C ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( B +s C ) e. No ) with typecode |-
232		addscl	Could not format ( ( A e. No /\ C e. No ) -> ( A +s C ) e. No ) : No typesetting found for |- ( ( A e. No /\ C e. No ) -> ( A +s C ) e. No ) with typecode |-
233	232	3adant2	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A +s C ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A +s C ) e. No ) with typecode |-
234		sltnle	Could not format ( ( ( B +s C ) e. No /\ ( A +s C ) e. No ) -> ( ( B +s C ) -. ( A +s C ) <_s ( B +s C ) ) ) : No typesetting found for |- ( ( ( B +s C ) e. No /\ ( A +s C ) e. No ) -> ( ( B +s C ) -. ( A +s C ) <_s ( B +s C ) ) ) with typecode |-
235	231 233 234	syl2anc	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( B +s C ) -. ( A +s C ) <_s ( B +s C ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( B +s C ) -. ( A +s C ) <_s ( B +s C ) ) ) with typecode |-
236		sltnle	$$⊢\left(B\in \mathrm{No}\wedge A\in \mathrm{No}\right)\to \left(B{<}_{s}A\leftrightarrow \neg A{\le }_{s}B\right)$$
237	236	ancoms	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to \left(B{<}_{s}A\leftrightarrow \neg A{\le }_{s}B\right)$$
238	237	3adant3	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\wedge C\in \mathrm{No}\right)\to \left(B{<}_{s}A\leftrightarrow \neg A{\le }_{s}B\right)$$
239	229 235 238	3imtr3d	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( -. ( A +s C ) <_s ( B +s C ) -> -. A <_s B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( -. ( A +s C ) <_s ( B +s C ) -> -. A <_s B ) ) with typecode |-
240	239	con4d	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A <_s B -> ( A +s C ) <_s ( B +s C ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A <_s B -> ( A +s C ) <_s ( B +s C ) ) ) with typecode |-
241		sleadd1im	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) <_s ( B +s C ) -> A <_s B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) <_s ( B +s C ) -> A <_s B ) ) with typecode |-
242	240 241	impbid	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A <_s B <-> ( A +s C ) <_s ( B +s C ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A <_s B <-> ( A +s C ) <_s ( B +s C ) ) ) with typecode |-