Step |
Hyp |
Ref |
Expression |
1 |
|
gsumzoppg.b |
|
2 |
|
gsumzoppg.0 |
|
3 |
|
gsumzoppg.z |
|
4 |
|
gsumzoppg.o |
|
5 |
|
gsumzoppg.g |
|
6 |
|
gsumzoppg.a |
|
7 |
|
gsumzoppg.f |
|
8 |
|
gsumzoppg.c |
|
9 |
|
gsumzoppg.n |
|
10 |
4
|
oppgmnd |
|
11 |
5 10
|
syl |
|
12 |
4 2
|
oppgid |
|
13 |
12
|
gsumz |
|
14 |
11 6 13
|
syl2anc |
|
15 |
2
|
gsumz |
|
16 |
5 6 15
|
syl2anc |
|
17 |
14 16
|
eqtr4d |
|
18 |
17
|
adantr |
|
19 |
2
|
fvexi |
|
20 |
19
|
a1i |
|
21 |
|
ssid |
|
22 |
|
fex |
|
23 |
7 6 22
|
syl2anc |
|
24 |
|
suppimacnv |
|
25 |
23 19 24
|
sylancl |
|
26 |
25
|
sseq1d |
|
27 |
21 26
|
mpbiri |
|
28 |
7 6 20 27
|
gsumcllem |
|
29 |
28
|
oveq2d |
|
30 |
28
|
oveq2d |
|
31 |
18 29 30
|
3eqtr4d |
|
32 |
31
|
ex |
|
33 |
|
simprl |
|
34 |
|
nnuz |
|
35 |
33 34
|
eleqtrdi |
|
36 |
7
|
adantr |
|
37 |
|
ffn |
|
38 |
|
dffn4 |
|
39 |
37 38
|
sylib |
|
40 |
|
fof |
|
41 |
36 39 40
|
3syl |
|
42 |
5
|
adantr |
|
43 |
1
|
submacs |
|
44 |
|
acsmre |
|
45 |
42 43 44
|
3syl |
|
46 |
|
eqid |
|
47 |
36
|
frnd |
|
48 |
45 46 47
|
mrcssidd |
|
49 |
41 48
|
fssd |
|
50 |
|
f1of1 |
|
51 |
50
|
ad2antll |
|
52 |
|
cnvimass |
|
53 |
52 36
|
fssdm |
|
54 |
|
f1ss |
|
55 |
51 53 54
|
syl2anc |
|
56 |
|
f1f |
|
57 |
55 56
|
syl |
|
58 |
|
fco |
|
59 |
49 57 58
|
syl2anc |
|
60 |
59
|
ffvelrnda |
|
61 |
46
|
mrccl |
|
62 |
45 47 61
|
syl2anc |
|
63 |
4
|
oppgsubm |
|
64 |
62 63
|
eleqtrdi |
|
65 |
|
eqid |
|
66 |
65
|
submcl |
|
67 |
66
|
3expb |
|
68 |
64 67
|
sylan |
|
69 |
|
eqid |
|
70 |
69 4 65
|
oppgplus |
|
71 |
8
|
adantr |
|
72 |
|
eqid |
|
73 |
3 46 72
|
cntzspan |
|
74 |
42 71 73
|
syl2anc |
|
75 |
72 3
|
submcmn2 |
|
76 |
62 75
|
syl |
|
77 |
74 76
|
mpbid |
|
78 |
77
|
sselda |
|
79 |
69 3
|
cntzi |
|
80 |
78 79
|
sylan |
|
81 |
70 80
|
eqtr4id |
|
82 |
81
|
anasss |
|
83 |
35 60 68 82
|
seqfeq4 |
|
84 |
4 1
|
oppgbas |
|
85 |
|
eqid |
|
86 |
42 10
|
syl |
|
87 |
6
|
adantr |
|
88 |
4 3
|
oppgcntz |
|
89 |
71 88
|
sseqtrdi |
|
90 |
|
suppssdm |
|
91 |
25 90
|
eqsstrrdi |
|
92 |
7 91
|
fssdmd |
|
93 |
92
|
adantr |
|
94 |
51 93 54
|
syl2anc |
|
95 |
26
|
adantr |
|
96 |
21 95
|
mpbiri |
|
97 |
|
f1ofo |
|
98 |
|
forn |
|
99 |
97 98
|
syl |
|
100 |
99
|
sseq2d |
|
101 |
100
|
ad2antll |
|
102 |
96 101
|
mpbird |
|
103 |
|
eqid |
|
104 |
84 12 65 85 86 87 36 89 33 94 102 103
|
gsumval3 |
|
105 |
27
|
adantr |
|
106 |
105 101
|
mpbird |
|
107 |
1 2 69 3 42 87 36 71 33 94 106 103
|
gsumval3 |
|
108 |
83 104 107
|
3eqtr4d |
|
109 |
108
|
expr |
|
110 |
109
|
exlimdv |
|
111 |
110
|
expimpd |
|
112 |
9
|
fsuppimpd |
|
113 |
25 112
|
eqeltrrd |
|
114 |
|
fz1f1o |
|
115 |
113 114
|
syl |
|
116 |
32 111 115
|
mpjaod |
|