Step |
Hyp |
Ref |
Expression |
1 |
|
prodfn0.1 |
|
2 |
|
prodfn0.2 |
|
3 |
|
prodfn0.3 |
|
4 |
|
prodfrec.4 |
|
5 |
|
eluzfz2 |
|
6 |
1 5
|
syl |
|
7 |
|
fveq2 |
|
8 |
|
fveq2 |
|
9 |
8
|
oveq2d |
|
10 |
7 9
|
eqeq12d |
|
11 |
10
|
imbi2d |
|
12 |
|
fveq2 |
|
13 |
|
fveq2 |
|
14 |
13
|
oveq2d |
|
15 |
12 14
|
eqeq12d |
|
16 |
15
|
imbi2d |
|
17 |
|
fveq2 |
|
18 |
|
fveq2 |
|
19 |
18
|
oveq2d |
|
20 |
17 19
|
eqeq12d |
|
21 |
20
|
imbi2d |
|
22 |
|
fveq2 |
|
23 |
|
fveq2 |
|
24 |
23
|
oveq2d |
|
25 |
22 24
|
eqeq12d |
|
26 |
25
|
imbi2d |
|
27 |
|
eluzfz1 |
|
28 |
1 27
|
syl |
|
29 |
|
fveq2 |
|
30 |
|
fveq2 |
|
31 |
30
|
oveq2d |
|
32 |
29 31
|
eqeq12d |
|
33 |
32
|
imbi2d |
|
34 |
4
|
expcom |
|
35 |
33 34
|
vtoclga |
|
36 |
28 35
|
mpcom |
|
37 |
|
eluzel2 |
|
38 |
1 37
|
syl |
|
39 |
|
seq1 |
|
40 |
38 39
|
syl |
|
41 |
|
seq1 |
|
42 |
38 41
|
syl |
|
43 |
42
|
oveq2d |
|
44 |
36 40 43
|
3eqtr4d |
|
45 |
44
|
a1i |
|
46 |
|
oveq1 |
|
47 |
46
|
3ad2ant3 |
|
48 |
|
fzofzp1 |
|
49 |
|
fveq2 |
|
50 |
|
fveq2 |
|
51 |
50
|
oveq2d |
|
52 |
49 51
|
eqeq12d |
|
53 |
52
|
imbi2d |
|
54 |
53 34
|
vtoclga |
|
55 |
48 54
|
syl |
|
56 |
55
|
impcom |
|
57 |
56
|
oveq2d |
|
58 |
|
1cnd |
|
59 |
|
elfzouz |
|
60 |
59
|
adantl |
|
61 |
|
elfzouz2 |
|
62 |
|
fzss2 |
|
63 |
61 62
|
syl |
|
64 |
63
|
sselda |
|
65 |
64 2
|
sylan2 |
|
66 |
65
|
anassrs |
|
67 |
|
mulcl |
|
68 |
67
|
adantl |
|
69 |
60 66 68
|
seqcl |
|
70 |
50
|
eleq1d |
|
71 |
70
|
imbi2d |
|
72 |
2
|
expcom |
|
73 |
71 72
|
vtoclga |
|
74 |
48 73
|
syl |
|
75 |
74
|
impcom |
|
76 |
64 3
|
sylan2 |
|
77 |
76
|
anassrs |
|
78 |
60 66 77
|
prodfn0 |
|
79 |
50
|
neeq1d |
|
80 |
79
|
imbi2d |
|
81 |
3
|
expcom |
|
82 |
80 81
|
vtoclga |
|
83 |
48 82
|
syl |
|
84 |
83
|
impcom |
|
85 |
58 69 58 75 78 84
|
divmuldivd |
|
86 |
|
1t1e1 |
|
87 |
86
|
oveq1i |
|
88 |
85 87
|
eqtrdi |
|
89 |
57 88
|
eqtrd |
|
90 |
89
|
3adant3 |
|
91 |
47 90
|
eqtrd |
|
92 |
|
seqp1 |
|
93 |
59 92
|
syl |
|
94 |
93
|
3ad2ant2 |
|
95 |
|
seqp1 |
|
96 |
59 95
|
syl |
|
97 |
96
|
oveq2d |
|
98 |
97
|
3ad2ant2 |
|
99 |
91 94 98
|
3eqtr4d |
|
100 |
99
|
3exp |
|
101 |
100
|
com12 |
|
102 |
101
|
a2d |
|
103 |
11 16 21 26 45 102
|
fzind2 |
|
104 |
6 103
|
mpcom |
|