Step |
Hyp |
Ref |
Expression |
1 |
|
gsumwspan.b |
|
2 |
|
gsumwspan.k |
|
3 |
1
|
submacs |
|
4 |
3
|
acsmred |
|
5 |
4
|
adantr |
|
6 |
|
simpr |
|
7 |
6
|
s1cld |
|
8 |
|
ssel2 |
|
9 |
8
|
adantll |
|
10 |
1
|
gsumws1 |
|
11 |
9 10
|
syl |
|
12 |
11
|
eqcomd |
|
13 |
|
oveq2 |
|
14 |
13
|
rspceeqv |
|
15 |
7 12 14
|
syl2anc |
|
16 |
|
eqid |
|
17 |
16
|
elrnmpt |
|
18 |
17
|
elv |
|
19 |
15 18
|
sylibr |
|
20 |
19
|
ex |
|
21 |
20
|
ssrdv |
|
22 |
2
|
mrccl |
|
23 |
4 22
|
sylan |
|
24 |
2
|
mrcssid |
|
25 |
4 24
|
sylan |
|
26 |
|
sswrd |
|
27 |
25 26
|
syl |
|
28 |
27
|
sselda |
|
29 |
|
gsumwsubmcl |
|
30 |
23 28 29
|
syl2an2r |
|
31 |
30
|
fmpttd |
|
32 |
31
|
frnd |
|
33 |
4 2
|
mrcssvd |
|
34 |
33
|
adantr |
|
35 |
32 34
|
sstrd |
|
36 |
|
wrd0 |
|
37 |
|
eqid |
|
38 |
37
|
gsum0 |
|
39 |
38
|
eqcomi |
|
40 |
39
|
a1i |
|
41 |
|
oveq2 |
|
42 |
41
|
rspceeqv |
|
43 |
36 40 42
|
sylancr |
|
44 |
|
fvex |
|
45 |
16
|
elrnmpt |
|
46 |
44 45
|
ax-mp |
|
47 |
43 46
|
sylibr |
|
48 |
|
ccatcl |
|
49 |
|
simpll |
|
50 |
|
sswrd |
|
51 |
50
|
ad2antlr |
|
52 |
|
simprl |
|
53 |
51 52
|
sseldd |
|
54 |
|
simprr |
|
55 |
51 54
|
sseldd |
|
56 |
|
eqid |
|
57 |
1 56
|
gsumccat |
|
58 |
49 53 55 57
|
syl3anc |
|
59 |
58
|
eqcomd |
|
60 |
|
oveq2 |
|
61 |
60
|
rspceeqv |
|
62 |
48 59 61
|
syl2an2 |
|
63 |
|
ovex |
|
64 |
16
|
elrnmpt |
|
65 |
63 64
|
ax-mp |
|
66 |
62 65
|
sylibr |
|
67 |
66
|
ralrimivva |
|
68 |
|
oveq2 |
|
69 |
68
|
cbvmptv |
|
70 |
69
|
rneqi |
|
71 |
70
|
raleqi |
|
72 |
|
oveq2 |
|
73 |
72
|
cbvmptv |
|
74 |
73
|
rneqi |
|
75 |
74
|
raleqi |
|
76 |
|
eqid |
|
77 |
|
oveq2 |
|
78 |
77
|
eleq1d |
|
79 |
76 78
|
ralrnmptw |
|
80 |
|
ovexd |
|
81 |
79 80
|
mprg |
|
82 |
75 81
|
bitri |
|
83 |
82
|
ralbii |
|
84 |
|
eqid |
|
85 |
|
oveq1 |
|
86 |
85
|
eleq1d |
|
87 |
86
|
ralbidv |
|
88 |
84 87
|
ralrnmptw |
|
89 |
|
ovexd |
|
90 |
88 89
|
mprg |
|
91 |
71 83 90
|
3bitri |
|
92 |
67 91
|
sylibr |
|
93 |
1 37 56
|
issubm |
|
94 |
93
|
adantr |
|
95 |
35 47 92 94
|
mpbir3and |
|
96 |
2
|
mrcsscl |
|
97 |
5 21 95 96
|
syl3anc |
|
98 |
97 32
|
eqssd |
|