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 |
|
gsumzcl.w |
|
9 |
|
gsumzf1o.h |
|
10 |
2
|
gsumz |
|
11 |
4 5 10
|
syl2anc |
|
12 |
|
f1of1 |
|
13 |
9 12
|
syl |
|
14 |
|
f1dmex |
|
15 |
13 5 14
|
syl2anc |
|
16 |
2
|
gsumz |
|
17 |
4 15 16
|
syl2anc |
|
18 |
11 17
|
eqtr4d |
|
19 |
18
|
adantr |
|
20 |
2
|
fvexi |
|
21 |
20
|
a1i |
|
22 |
|
ssidd |
|
23 |
6 5 21 22
|
gsumcllem |
|
24 |
23
|
oveq2d |
|
25 |
|
f1of |
|
26 |
9 25
|
syl |
|
27 |
26
|
adantr |
|
28 |
27
|
ffvelrnda |
|
29 |
27
|
feqmptd |
|
30 |
|
eqidd |
|
31 |
28 29 23 30
|
fmptco |
|
32 |
31
|
oveq2d |
|
33 |
19 24 32
|
3eqtr4d |
|
34 |
33
|
ex |
|
35 |
|
coass |
|
36 |
9
|
adantr |
|
37 |
|
f1ococnv2 |
|
38 |
36 37
|
syl |
|
39 |
38
|
coeq1d |
|
40 |
|
f1of1 |
|
41 |
40
|
ad2antll |
|
42 |
|
suppssdm |
|
43 |
42 6
|
fssdm |
|
44 |
43
|
adantr |
|
45 |
|
f1ss |
|
46 |
41 44 45
|
syl2anc |
|
47 |
|
f1f |
|
48 |
|
fcoi2 |
|
49 |
46 47 48
|
3syl |
|
50 |
39 49
|
eqtrd |
|
51 |
35 50
|
syl5reqr |
|
52 |
51
|
coeq2d |
|
53 |
|
coass |
|
54 |
52 53
|
eqtr4di |
|
55 |
54
|
seqeq3d |
|
56 |
55
|
fveq1d |
|
57 |
|
eqid |
|
58 |
4
|
adantr |
|
59 |
5
|
adantr |
|
60 |
6
|
adantr |
|
61 |
7
|
adantr |
|
62 |
|
simprl |
|
63 |
|
ssid |
|
64 |
|
f1ofo |
|
65 |
|
forn |
|
66 |
64 65
|
syl |
|
67 |
66
|
ad2antll |
|
68 |
63 67
|
sseqtrrid |
|
69 |
|
eqid |
|
70 |
1 2 57 3 58 59 60 61 62 46 68 69
|
gsumval3 |
|
71 |
15
|
adantr |
|
72 |
|
fco |
|
73 |
6 26 72
|
syl2anc |
|
74 |
73
|
adantr |
|
75 |
|
rncoss |
|
76 |
3
|
cntzidss |
|
77 |
7 75 76
|
sylancl |
|
78 |
77
|
adantr |
|
79 |
|
f1ocnv |
|
80 |
|
f1of1 |
|
81 |
9 79 80
|
3syl |
|
82 |
81
|
adantr |
|
83 |
|
f1co |
|
84 |
82 46 83
|
syl2anc |
|
85 |
|
ssidd |
|
86 |
|
fex |
|
87 |
6 5 86
|
syl2anc |
|
88 |
|
suppimacnv |
|
89 |
87 20 88
|
sylancl |
|
90 |
89
|
eqcomd |
|
91 |
90
|
adantr |
|
92 |
85 91 67
|
3sstr4d |
|
93 |
|
imass2 |
|
94 |
92 93
|
syl |
|
95 |
|
cnvco |
|
96 |
95
|
imaeq1i |
|
97 |
|
imaco |
|
98 |
96 97
|
eqtri |
|
99 |
|
rnco2 |
|
100 |
94 98 99
|
3sstr4g |
|
101 |
|
f1oexrnex |
|
102 |
9 5 101
|
syl2anc |
|
103 |
|
coexg |
|
104 |
87 102 103
|
syl2anc |
|
105 |
|
suppimacnv |
|
106 |
104 20 105
|
sylancl |
|
107 |
106
|
sseq1d |
|
108 |
107
|
adantr |
|
109 |
100 108
|
mpbird |
|
110 |
|
eqid |
|
111 |
1 2 57 3 58 71 74 78 62 84 109 110
|
gsumval3 |
|
112 |
56 70 111
|
3eqtr4d |
|
113 |
112
|
expr |
|
114 |
113
|
exlimdv |
|
115 |
114
|
expimpd |
|
116 |
|
fsuppimp |
|
117 |
116
|
simprd |
|
118 |
|
fz1f1o |
|
119 |
8 117 118
|
3syl |
|
120 |
34 115 119
|
mpjaod |
|