Step |
Hyp |
Ref |
Expression |
1 |
|
df-4 |
|
2 |
1
|
fveq2i |
Could not format ( Ack ` 4 ) = ( Ack ` ( 3 + 1 ) ) : No typesetting found for |- ( Ack ` 4 ) = ( Ack ` ( 3 + 1 ) ) with typecode |- |
3 |
|
df-2 |
|
4 |
2 3
|
fveq12i |
Could not format ( ( Ack ` 4 ) ` 2 ) = ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) : No typesetting found for |- ( ( Ack ` 4 ) ` 2 ) = ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) with typecode |- |
5 |
|
3nn0 |
|
6 |
|
1nn0 |
|
7 |
|
ackvalsucsucval |
Could not format ( ( 3 e. NN0 /\ 1 e. NN0 ) -> ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) = ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) ) : No typesetting found for |- ( ( 3 e. NN0 /\ 1 e. NN0 ) -> ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) = ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) ) with typecode |- |
8 |
5 6 7
|
mp2an |
Could not format ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) = ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) : No typesetting found for |- ( ( Ack ` ( 3 + 1 ) ) ` ( 1 + 1 ) ) = ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) with typecode |- |
9 |
|
3p1e4 |
|
10 |
9
|
fveq2i |
Could not format ( Ack ` ( 3 + 1 ) ) = ( Ack ` 4 ) : No typesetting found for |- ( Ack ` ( 3 + 1 ) ) = ( Ack ` 4 ) with typecode |- |
11 |
10
|
fveq1i |
Could not format ( ( Ack ` ( 3 + 1 ) ) ` 1 ) = ( ( Ack ` 4 ) ` 1 ) : No typesetting found for |- ( ( Ack ` ( 3 + 1 ) ) ` 1 ) = ( ( Ack ` 4 ) ` 1 ) with typecode |- |
12 |
|
ackval41a |
Could not format ( ( Ack ` 4 ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` 4 ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) with typecode |- |
13 |
11 12
|
eqtri |
Could not format ( ( Ack ` ( 3 + 1 ) ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` ( 3 + 1 ) ) ` 1 ) = ( ( 2 ^ ; 1 6 ) - 3 ) with typecode |- |
14 |
13
|
fveq2i |
Could not format ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) = ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) : No typesetting found for |- ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) = ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) with typecode |- |
15 |
|
2cn |
|
16 |
|
6nn0 |
|
17 |
6 16
|
deccl |
|
18 |
|
expcl |
|
19 |
15 17 18
|
mp2an |
|
20 |
|
3cn |
|
21 |
|
ackval3 |
Could not format ( Ack ` 3 ) = ( n e. NN0 |-> ( ( 2 ^ ( n + 3 ) ) - 3 ) ) : No typesetting found for |- ( Ack ` 3 ) = ( n e. NN0 |-> ( ( 2 ^ ( n + 3 ) ) - 3 ) ) with typecode |- |
22 |
|
oveq1 |
|
23 |
|
npcan |
|
24 |
22 23
|
sylan9eqr |
|
25 |
24
|
oveq2d |
|
26 |
25
|
oveq1d |
|
27 |
|
3re |
|
28 |
|
4re |
|
29 |
|
3lt4 |
|
30 |
27 28 29
|
ltleii |
|
31 |
|
sq2 |
|
32 |
30 31
|
breqtrri |
|
33 |
|
2re |
|
34 |
|
1le2 |
|
35 |
17
|
nn0zi |
|
36 |
|
1nn |
|
37 |
|
2nn0 |
|
38 |
|
9re |
|
39 |
|
2lt9 |
|
40 |
33 38 39
|
ltleii |
|
41 |
36 16 37 40
|
declei |
|
42 |
|
2z |
|
43 |
42
|
eluz1i |
|
44 |
35 41 43
|
mpbir2an |
|
45 |
|
leexp2a |
|
46 |
33 34 44 45
|
mp3an |
|
47 |
|
4nn0 |
|
48 |
31 47
|
eqeltri |
|
49 |
48
|
nn0rei |
|
50 |
37 17
|
nn0expcli |
|
51 |
50
|
nn0rei |
|
52 |
27 49 51
|
letri |
|
53 |
32 46 52
|
mp2an |
|
54 |
|
nn0sub |
|
55 |
5 50 54
|
mp2an |
|
56 |
53 55
|
mpbi |
|
57 |
56
|
a1i |
|
58 |
|
ovexd |
|
59 |
21 26 57 58
|
fvmptd2 |
Could not format ( ( ( 2 ^ ; 1 6 ) e. CC /\ 3 e. CC ) -> ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) = ( ( 2 ^ ( 2 ^ ; 1 6 ) ) - 3 ) ) : No typesetting found for |- ( ( ( 2 ^ ; 1 6 ) e. CC /\ 3 e. CC ) -> ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) = ( ( 2 ^ ( 2 ^ ; 1 6 ) ) - 3 ) ) with typecode |- |
60 |
19 20 59
|
mp2an |
Could not format ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) = ( ( 2 ^ ( 2 ^ ; 1 6 ) ) - 3 ) : No typesetting found for |- ( ( Ack ` 3 ) ` ( ( 2 ^ ; 1 6 ) - 3 ) ) = ( ( 2 ^ ( 2 ^ ; 1 6 ) ) - 3 ) with typecode |- |
61 |
|
2exp16 |
|
62 |
61
|
oveq2i |
|
63 |
62
|
oveq1i |
|
64 |
14 60 63
|
3eqtri |
Could not format ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` 3 ) ` ( ( Ack ` ( 3 + 1 ) ) ` 1 ) ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) with typecode |- |
65 |
4 8 64
|
3eqtri |
Could not format ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) : No typesetting found for |- ( ( Ack ` 4 ) ` 2 ) = ( ( 2 ^ ; ; ; ; 6 5 5 3 6 ) - 3 ) with typecode |- |