Step |
Hyp |
Ref |
Expression |
0 |
|
cmvr |
|- mVar |
1 |
|
vi |
|- i |
2 |
|
cvv |
|- _V |
3 |
|
vr |
|- r |
4 |
|
vx |
|- x |
5 |
1
|
cv |
|- i |
6 |
|
vf |
|- f |
7 |
|
vh |
|- h |
8 |
|
cn0 |
|- NN0 |
9 |
|
cmap |
|- ^m |
10 |
8 5 9
|
co |
|- ( NN0 ^m i ) |
11 |
7
|
cv |
|- h |
12 |
11
|
ccnv |
|- `' h |
13 |
|
cn |
|- NN |
14 |
12 13
|
cima |
|- ( `' h " NN ) |
15 |
|
cfn |
|- Fin |
16 |
14 15
|
wcel |
|- ( `' h " NN ) e. Fin |
17 |
16 7 10
|
crab |
|- { h e. ( NN0 ^m i ) | ( `' h " NN ) e. Fin } |
18 |
6
|
cv |
|- f |
19 |
|
vy |
|- y |
20 |
19
|
cv |
|- y |
21 |
4
|
cv |
|- x |
22 |
20 21
|
wceq |
|- y = x |
23 |
|
c1 |
|- 1 |
24 |
|
cc0 |
|- 0 |
25 |
22 23 24
|
cif |
|- if ( y = x , 1 , 0 ) |
26 |
19 5 25
|
cmpt |
|- ( y e. i |-> if ( y = x , 1 , 0 ) ) |
27 |
18 26
|
wceq |
|- f = ( y e. i |-> if ( y = x , 1 , 0 ) ) |
28 |
|
cur |
|- 1r |
29 |
3
|
cv |
|- r |
30 |
29 28
|
cfv |
|- ( 1r ` r ) |
31 |
|
c0g |
|- 0g |
32 |
29 31
|
cfv |
|- ( 0g ` r ) |
33 |
27 30 32
|
cif |
|- if ( f = ( y e. i |-> if ( y = x , 1 , 0 ) ) , ( 1r ` r ) , ( 0g ` r ) ) |
34 |
6 17 33
|
cmpt |
|- ( f e. { h e. ( NN0 ^m i ) | ( `' h " NN ) e. Fin } |-> if ( f = ( y e. i |-> if ( y = x , 1 , 0 ) ) , ( 1r ` r ) , ( 0g ` r ) ) ) |
35 |
4 5 34
|
cmpt |
|- ( x e. i |-> ( f e. { h e. ( NN0 ^m i ) | ( `' h " NN ) e. Fin } |-> if ( f = ( y e. i |-> if ( y = x , 1 , 0 ) ) , ( 1r ` r ) , ( 0g ` r ) ) ) ) |
36 |
1 3 2 2 35
|
cmpo |
|- ( i e. _V , r e. _V |-> ( x e. i |-> ( f e. { h e. ( NN0 ^m i ) | ( `' h " NN ) e. Fin } |-> if ( f = ( y e. i |-> if ( y = x , 1 , 0 ) ) , ( 1r ` r ) , ( 0g ` r ) ) ) ) ) |
37 |
0 36
|
wceq |
|- mVar = ( i e. _V , r e. _V |-> ( x e. i |-> ( f e. { h e. ( NN0 ^m i ) | ( `' h " NN ) e. Fin } |-> if ( f = ( y e. i |-> if ( y = x , 1 , 0 ) ) , ( 1r ` r ) , ( 0g ` r ) ) ) ) ) |