Step |
Hyp |
Ref |
Expression |
1 |
|
knoppndvlem7.t |
|
2 |
|
knoppndvlem7.f |
|
3 |
|
knoppndvlem7.a |
|
4 |
|
knoppndvlem7.j |
|
5 |
|
knoppndvlem7.m |
|
6 |
|
knoppndvlem7.n |
|
7 |
3
|
a1i |
|
8 |
4
|
nn0zd |
|
9 |
6 8 5
|
knoppndvlem1 |
|
10 |
7 9
|
eqeltrd |
|
11 |
2 10 4
|
knoppcnlem1 |
|
12 |
3
|
oveq2i |
|
13 |
12
|
a1i |
|
14 |
|
2cnd |
|
15 |
|
nnz |
|
16 |
6 15
|
syl |
|
17 |
16
|
zcnd |
|
18 |
14 17
|
mulcld |
|
19 |
18 4
|
expcld |
|
20 |
|
2ne0 |
|
21 |
20
|
a1i |
|
22 |
|
0red |
|
23 |
|
1red |
|
24 |
16
|
zred |
|
25 |
|
0lt1 |
|
26 |
25
|
a1i |
|
27 |
|
nnge1 |
|
28 |
6 27
|
syl |
|
29 |
22 23 24 26 28
|
ltletrd |
|
30 |
22 29
|
ltned |
|
31 |
30
|
necomd |
|
32 |
14 17 21 31
|
mulne0d |
|
33 |
8
|
znegcld |
|
34 |
18 32 33
|
expclzd |
|
35 |
34 14 21
|
divcld |
|
36 |
5
|
zcnd |
|
37 |
19 35 36
|
mulassd |
|
38 |
37
|
eqcomd |
|
39 |
19 34 14 21
|
divassd |
|
40 |
39
|
eqcomd |
|
41 |
18 32 8
|
expnegd |
|
42 |
41
|
oveq2d |
|
43 |
18 32 8
|
expne0d |
|
44 |
19 43
|
recidd |
|
45 |
42 44
|
eqtrd |
|
46 |
45
|
oveq1d |
|
47 |
40 46
|
eqtrd |
|
48 |
47
|
oveq1d |
|
49 |
36 14 21
|
divrec2d |
|
50 |
49
|
eqcomd |
|
51 |
38 48 50
|
3eqtrd |
|
52 |
13 51
|
eqtrd |
|
53 |
52
|
fveq2d |
|
54 |
53
|
oveq2d |
|
55 |
11 54
|
eqtrd |
|