Step |
Hyp |
Ref |
Expression |
1 |
|
gsumzcl.b |
|
2 |
|
gsumzcl.0 |
|
3 |
|
gsumzcl.z |
|
4 |
|
gsumzcl.g |
|
5 |
|
gsumzcl.a |
|
6 |
|
gsumzcl.f |
|
7 |
|
gsumzcl.c |
|
8 |
|
gsumzres.s |
|
9 |
|
gsumzres.w |
|
10 |
|
inex1g |
|
11 |
5 10
|
syl |
|
12 |
2
|
gsumz |
|
13 |
4 11 12
|
syl2anc |
|
14 |
2
|
gsumz |
|
15 |
4 5 14
|
syl2anc |
|
16 |
13 15
|
eqtr4d |
|
17 |
16
|
adantr |
|
18 |
|
resres |
|
19 |
|
ffn |
|
20 |
|
fnresdm |
|
21 |
6 19 20
|
3syl |
|
22 |
21
|
reseq1d |
|
23 |
18 22
|
syl5eqr |
|
24 |
23
|
adantr |
|
25 |
2
|
fvexi |
|
26 |
25
|
a1i |
|
27 |
|
ssid |
|
28 |
27
|
a1i |
|
29 |
6 5 26 28
|
gsumcllem |
|
30 |
29
|
reseq1d |
|
31 |
|
inss1 |
|
32 |
|
resmpt |
|
33 |
31 32
|
ax-mp |
|
34 |
30 33
|
eqtrdi |
|
35 |
24 34
|
eqtr3d |
|
36 |
35
|
oveq2d |
|
37 |
29
|
oveq2d |
|
38 |
17 36 37
|
3eqtr4d |
|
39 |
38
|
ex |
|
40 |
|
f1ofo |
|
41 |
|
forn |
|
42 |
40 41
|
syl |
|
43 |
42
|
ad2antll |
|
44 |
8
|
adantr |
|
45 |
43 44
|
eqsstrd |
|
46 |
|
cores |
|
47 |
45 46
|
syl |
|
48 |
47
|
seqeq3d |
|
49 |
48
|
fveq1d |
|
50 |
|
eqid |
|
51 |
4
|
adantr |
|
52 |
11
|
adantr |
|
53 |
6
|
adantr |
|
54 |
|
fssres |
|
55 |
53 31 54
|
sylancl |
|
56 |
23
|
feq1d |
|
57 |
56
|
biimpa |
|
58 |
55 57
|
syldan |
|
59 |
|
resss |
|
60 |
59
|
rnssi |
|
61 |
3
|
cntzidss |
|
62 |
7 60 61
|
sylancl |
|
63 |
62
|
adantr |
|
64 |
|
simprl |
|
65 |
|
f1of1 |
|
66 |
65
|
ad2antll |
|
67 |
|
suppssdm |
|
68 |
67 6
|
fssdm |
|
69 |
68 8
|
ssind |
|
70 |
69
|
adantr |
|
71 |
|
f1ss |
|
72 |
66 70 71
|
syl2anc |
|
73 |
|
fex |
|
74 |
6 5 73
|
syl2anc |
|
75 |
|
ressuppss |
|
76 |
74 25 75
|
sylancl |
|
77 |
|
sseq2 |
|
78 |
76 77
|
syl5ibr |
|
79 |
40 41 78
|
3syl |
|
80 |
79
|
adantl |
|
81 |
80
|
impcom |
|
82 |
|
eqid |
|
83 |
1 2 50 3 51 52 58 63 64 72 81 82
|
gsumval3 |
|
84 |
5
|
adantr |
|
85 |
7
|
adantr |
|
86 |
68
|
adantr |
|
87 |
|
f1ss |
|
88 |
66 86 87
|
syl2anc |
|
89 |
27 43
|
sseqtrrid |
|
90 |
|
eqid |
|
91 |
1 2 50 3 51 84 53 85 64 88 89 90
|
gsumval3 |
|
92 |
49 83 91
|
3eqtr4d |
|
93 |
92
|
expr |
|
94 |
93
|
exlimdv |
|
95 |
94
|
expimpd |
|
96 |
|
fsuppimp |
|
97 |
96
|
simprd |
|
98 |
|
fz1f1o |
|
99 |
9 97 98
|
3syl |
|
100 |
39 95 99
|
mpjaod |
|