Step |
Hyp |
Ref |
Expression |
1 |
|
oveq1 |
Could not format ( x = xO -> ( x x.s 1s ) = ( xO x.s 1s ) ) : No typesetting found for |- ( x = xO -> ( x x.s 1s ) = ( xO x.s 1s ) ) with typecode |- |
2 |
|
id |
Could not format ( x = xO -> x = xO ) : No typesetting found for |- ( x = xO -> x = xO ) with typecode |- |
3 |
1 2
|
eqeq12d |
Could not format ( x = xO -> ( ( x x.s 1s ) = x <-> ( xO x.s 1s ) = xO ) ) : No typesetting found for |- ( x = xO -> ( ( x x.s 1s ) = x <-> ( xO x.s 1s ) = xO ) ) with typecode |- |
4 |
|
oveq1 |
|
5 |
|
id |
|
6 |
4 5
|
eqeq12d |
|
7 |
|
1sno |
|
8 |
|
mulsval |
|
9 |
7 8
|
mpan2 |
|
10 |
9
|
adantr |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 1s ) = ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 1s ) = ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) ) ) with typecode |- |
11 |
|
elun1 |
|
12 |
|
oveq1 |
Could not format ( xO = p -> ( xO x.s 1s ) = ( p x.s 1s ) ) : No typesetting found for |- ( xO = p -> ( xO x.s 1s ) = ( p x.s 1s ) ) with typecode |- |
13 |
|
id |
Could not format ( xO = p -> xO = p ) : No typesetting found for |- ( xO = p -> xO = p ) with typecode |- |
14 |
12 13
|
eqeq12d |
Could not format ( xO = p -> ( ( xO x.s 1s ) = xO <-> ( p x.s 1s ) = p ) ) : No typesetting found for |- ( xO = p -> ( ( xO x.s 1s ) = xO <-> ( p x.s 1s ) = p ) ) with typecode |- |
15 |
14
|
rspcva |
Could not format ( ( p e. ( ( _Left ` x ) u. ( _Right ` x ) ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( p x.s 1s ) = p ) : No typesetting found for |- ( ( p e. ( ( _Left ` x ) u. ( _Right ` x ) ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( p x.s 1s ) = p ) with typecode |- |
16 |
11 15
|
sylan |
Could not format ( ( p e. ( _Left ` x ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( p x.s 1s ) = p ) : No typesetting found for |- ( ( p e. ( _Left ` x ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( p x.s 1s ) = p ) with typecode |- |
17 |
16
|
ancoms |
Could not format ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO /\ p e. ( _Left ` x ) ) -> ( p x.s 1s ) = p ) : No typesetting found for |- ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO /\ p e. ( _Left ` x ) ) -> ( p x.s 1s ) = p ) with typecode |- |
18 |
17
|
adantll |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p x.s 1s ) = p ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p x.s 1s ) = p ) with typecode |- |
19 |
|
muls01 |
|
20 |
19
|
adantr |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 0s ) = 0s ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 0s ) = 0s ) with typecode |- |
21 |
20
|
adantr |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( x x.s 0s ) = 0s ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( x x.s 0s ) = 0s ) with typecode |- |
22 |
18 21
|
oveq12d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( p x.s 1s ) +s ( x x.s 0s ) ) = ( p +s 0s ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( p x.s 1s ) +s ( x x.s 0s ) ) = ( p +s 0s ) ) with typecode |- |
23 |
|
leftssno |
|
24 |
23
|
sseli |
|
25 |
24
|
adantl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> p e. No ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> p e. No ) with typecode |- |
26 |
25
|
addsridd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p +s 0s ) = p ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p +s 0s ) = p ) with typecode |- |
27 |
22 26
|
eqtrd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( p x.s 1s ) +s ( x x.s 0s ) ) = p ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( p x.s 1s ) +s ( x x.s 0s ) ) = p ) with typecode |- |
28 |
|
muls01 |
|
29 |
25 28
|
syl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p x.s 0s ) = 0s ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p x.s 0s ) = 0s ) with typecode |- |
30 |
27 29
|
oveq12d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) = ( p -s 0s ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) = ( p -s 0s ) ) with typecode |- |
31 |
|
subsid1 |
|
32 |
25 31
|
syl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p -s 0s ) = p ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( p -s 0s ) = p ) with typecode |- |
33 |
30 32
|
eqtrd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) = p ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) = p ) with typecode |- |
34 |
33
|
eqeq2d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> a = p ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> a = p ) ) with typecode |- |
35 |
|
equcom |
|
36 |
34 35
|
bitrdi |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> p = a ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ p e. ( _Left ` x ) ) -> ( a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> p = a ) ) with typecode |- |
37 |
36
|
rexbidva |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. p e. ( _Left ` x ) a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> E. p e. ( _Left ` x ) p = a ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. p e. ( _Left ` x ) a = ( ( ( p x.s 1s ) +s ( x x.s 0s ) ) -s ( p x.s 0s ) ) <-> E. p e. ( _Left ` x ) p = a ) ) with typecode |- |
38 |
|
left1s |
|
39 |
38
|
rexeqi |
|
40 |
|
0sno |
|
41 |
40
|
elexi |
|
42 |
|
oveq2 |
|
43 |
42
|
oveq2d |
|
44 |
|
oveq2 |
|
45 |
43 44
|
oveq12d |
|
46 |
45
|
eqeq2d |
|
47 |
41 46
|
rexsn |
|
48 |
39 47
|
bitri |
|
49 |
48
|
rexbii |
|
50 |
|
risset |
|
51 |
37 49 50
|
3bitr4g |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) <-> a e. ( _Left ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) <-> a e. ( _Left ` x ) ) ) with typecode |- |
52 |
51
|
eqabcdv |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } = ( _Left ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } = ( _Left ` x ) ) with typecode |- |
53 |
|
rex0 |
|
54 |
|
right1s |
|
55 |
54
|
rexeqi |
|
56 |
53 55
|
mtbir |
|
57 |
56
|
a1i |
|
58 |
57
|
nrex |
|
59 |
58
|
abf |
|
60 |
59
|
a1i |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } = (/) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } = (/) ) with typecode |- |
61 |
52 60
|
uneq12d |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) = ( ( _Left ` x ) u. (/) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) = ( ( _Left ` x ) u. (/) ) ) with typecode |- |
62 |
|
un0 |
|
63 |
61 62
|
eqtrdi |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) = ( _Left ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) = ( _Left ` x ) ) with typecode |- |
64 |
|
rex0 |
|
65 |
54
|
rexeqi |
|
66 |
64 65
|
mtbir |
|
67 |
66
|
a1i |
|
68 |
67
|
nrex |
|
69 |
68
|
abf |
|
70 |
69
|
a1i |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } = (/) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } = (/) ) with typecode |- |
71 |
|
elun2 |
|
72 |
|
oveq1 |
Could not format ( xO = v -> ( xO x.s 1s ) = ( v x.s 1s ) ) : No typesetting found for |- ( xO = v -> ( xO x.s 1s ) = ( v x.s 1s ) ) with typecode |- |
73 |
|
id |
Could not format ( xO = v -> xO = v ) : No typesetting found for |- ( xO = v -> xO = v ) with typecode |- |
74 |
72 73
|
eqeq12d |
Could not format ( xO = v -> ( ( xO x.s 1s ) = xO <-> ( v x.s 1s ) = v ) ) : No typesetting found for |- ( xO = v -> ( ( xO x.s 1s ) = xO <-> ( v x.s 1s ) = v ) ) with typecode |- |
75 |
74
|
rspcva |
Could not format ( ( v e. ( ( _Left ` x ) u. ( _Right ` x ) ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( v x.s 1s ) = v ) : No typesetting found for |- ( ( v e. ( ( _Left ` x ) u. ( _Right ` x ) ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( v x.s 1s ) = v ) with typecode |- |
76 |
71 75
|
sylan |
Could not format ( ( v e. ( _Right ` x ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( v x.s 1s ) = v ) : No typesetting found for |- ( ( v e. ( _Right ` x ) /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( v x.s 1s ) = v ) with typecode |- |
77 |
76
|
ancoms |
Could not format ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO /\ v e. ( _Right ` x ) ) -> ( v x.s 1s ) = v ) : No typesetting found for |- ( ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO /\ v e. ( _Right ` x ) ) -> ( v x.s 1s ) = v ) with typecode |- |
78 |
77
|
adantll |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v x.s 1s ) = v ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v x.s 1s ) = v ) with typecode |- |
79 |
20
|
adantr |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( x x.s 0s ) = 0s ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( x x.s 0s ) = 0s ) with typecode |- |
80 |
78 79
|
oveq12d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( v x.s 1s ) +s ( x x.s 0s ) ) = ( v +s 0s ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( v x.s 1s ) +s ( x x.s 0s ) ) = ( v +s 0s ) ) with typecode |- |
81 |
|
rightssno |
|
82 |
81
|
sseli |
|
83 |
82
|
adantl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> v e. No ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> v e. No ) with typecode |- |
84 |
83
|
addsridd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v +s 0s ) = v ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v +s 0s ) = v ) with typecode |- |
85 |
80 84
|
eqtrd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( v x.s 1s ) +s ( x x.s 0s ) ) = v ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( v x.s 1s ) +s ( x x.s 0s ) ) = v ) with typecode |- |
86 |
|
muls01 |
|
87 |
83 86
|
syl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v x.s 0s ) = 0s ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v x.s 0s ) = 0s ) with typecode |- |
88 |
85 87
|
oveq12d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) = ( v -s 0s ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) = ( v -s 0s ) ) with typecode |- |
89 |
|
subsid1 |
|
90 |
83 89
|
syl |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v -s 0s ) = v ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( v -s 0s ) = v ) with typecode |- |
91 |
88 90
|
eqtrd |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) = v ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) = v ) with typecode |- |
92 |
91
|
eqeq2d |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( d = ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) <-> d = v ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( d = ( ( ( v x.s 1s ) +s ( x x.s 0s ) ) -s ( v x.s 0s ) ) <-> d = v ) ) with typecode |- |
93 |
38
|
rexeqi |
|
94 |
|
oveq2 |
|
95 |
94
|
oveq2d |
|
96 |
|
oveq2 |
|
97 |
95 96
|
oveq12d |
|
98 |
97
|
eqeq2d |
|
99 |
41 98
|
rexsn |
|
100 |
93 99
|
bitri |
|
101 |
|
equcom |
|
102 |
92 100 101
|
3bitr4g |
Could not format ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> v = d ) ) : No typesetting found for |- ( ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) /\ v e. ( _Right ` x ) ) -> ( E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> v = d ) ) with typecode |- |
103 |
102
|
rexbidva |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> E. v e. ( _Right ` x ) v = d ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> E. v e. ( _Right ` x ) v = d ) ) with typecode |- |
104 |
|
risset |
|
105 |
103 104
|
bitr4di |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> d e. ( _Right ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) <-> d e. ( _Right ` x ) ) ) with typecode |- |
106 |
105
|
eqabcdv |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } = ( _Right ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } = ( _Right ` x ) ) with typecode |- |
107 |
70 106
|
uneq12d |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) = ( (/) u. ( _Right ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) = ( (/) u. ( _Right ` x ) ) ) with typecode |- |
108 |
|
0un |
|
109 |
107 108
|
eqtrdi |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) = ( _Right ` x ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) = ( _Right ` x ) ) with typecode |- |
110 |
63 109
|
oveq12d |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) ) = ( ( _Left ` x ) |s ( _Right ` x ) ) ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` 1s ) a = ( ( ( p x.s 1s ) +s ( x x.s q ) ) -s ( p x.s q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` 1s ) b = ( ( ( r x.s 1s ) +s ( x x.s s ) ) -s ( r x.s s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` 1s ) c = ( ( ( t x.s 1s ) +s ( x x.s u ) ) -s ( t x.s u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` 1s ) d = ( ( ( v x.s 1s ) +s ( x x.s w ) ) -s ( v x.s w ) ) } ) ) = ( ( _Left ` x ) |s ( _Right ` x ) ) ) with typecode |- |
111 |
|
lrcut |
|
112 |
111
|
adantr |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( ( _Left ` x ) |s ( _Right ` x ) ) = x ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( ( _Left ` x ) |s ( _Right ` x ) ) = x ) with typecode |- |
113 |
10 110 112
|
3eqtrd |
Could not format ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 1s ) = x ) : No typesetting found for |- ( ( x e. No /\ A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO ) -> ( x x.s 1s ) = x ) with typecode |- |
114 |
113
|
ex |
Could not format ( x e. No -> ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO -> ( x x.s 1s ) = x ) ) : No typesetting found for |- ( x e. No -> ( A. xO e. ( ( _Left ` x ) u. ( _Right ` x ) ) ( xO x.s 1s ) = xO -> ( x x.s 1s ) = x ) ) with typecode |- |
115 |
3 6 114
|
noinds |
|