Step |
Hyp |
Ref |
Expression |
1 |
|
gsumwcl.b |
|
2 |
|
gsumsgrpccat.p |
|
3 |
|
oveq1 |
|
4 |
3
|
oveq2d |
|
5 |
|
oveq2 |
|
6 |
|
eqid |
|
7 |
6
|
gsum0 |
|
8 |
5 7
|
eqtrdi |
|
9 |
8
|
oveq1d |
|
10 |
4 9
|
eqeq12d |
|
11 |
|
oveq2 |
|
12 |
11
|
oveq2d |
|
13 |
|
oveq2 |
|
14 |
13 7
|
eqtrdi |
|
15 |
14
|
oveq2d |
|
16 |
12 15
|
eqeq12d |
|
17 |
|
simpl1 |
|
18 |
|
lennncl |
|
19 |
18
|
3ad2antl2 |
|
20 |
19
|
adantrr |
|
21 |
|
lennncl |
|
22 |
21
|
3ad2antl3 |
|
23 |
22
|
adantrl |
|
24 |
20 23
|
nnaddcld |
|
25 |
|
nnm1nn0 |
|
26 |
24 25
|
syl |
|
27 |
|
nn0uz |
|
28 |
26 27
|
eleqtrdi |
|
29 |
|
simpl2 |
|
30 |
|
simpl3 |
|
31 |
|
ccatcl |
|
32 |
29 30 31
|
syl2anc |
|
33 |
|
wrdf |
|
34 |
32 33
|
syl |
|
35 |
|
ccatlen |
|
36 |
29 30 35
|
syl2anc |
|
37 |
36
|
oveq2d |
|
38 |
20
|
nnzd |
|
39 |
23
|
nnzd |
|
40 |
38 39
|
zaddcld |
|
41 |
|
fzoval |
|
42 |
40 41
|
syl |
|
43 |
37 42
|
eqtrd |
|
44 |
43
|
feq2d |
|
45 |
34 44
|
mpbid |
|
46 |
1 2 17 28 45
|
gsumval2 |
|
47 |
|
nnm1nn0 |
|
48 |
20 47
|
syl |
|
49 |
48 27
|
eleqtrdi |
|
50 |
|
wrdf |
|
51 |
29 50
|
syl |
|
52 |
|
fzoval |
|
53 |
38 52
|
syl |
|
54 |
53
|
feq2d |
|
55 |
51 54
|
mpbid |
|
56 |
1 2 17 49 55
|
gsumval2 |
|
57 |
|
nnm1nn0 |
|
58 |
23 57
|
syl |
|
59 |
58 27
|
eleqtrdi |
|
60 |
|
wrdf |
|
61 |
30 60
|
syl |
|
62 |
|
fzoval |
|
63 |
39 62
|
syl |
|
64 |
63
|
feq2d |
|
65 |
61 64
|
mpbid |
|
66 |
1 2 17 59 65
|
gsumval2 |
|
67 |
56 66
|
oveq12d |
|
68 |
1 2
|
mndcl |
|
69 |
68
|
3expb |
|
70 |
17 69
|
sylan |
|
71 |
1 2
|
mndass |
|
72 |
17 71
|
sylan |
|
73 |
|
uzid |
|
74 |
38 73
|
syl |
|
75 |
|
uzaddcl |
|
76 |
74 58 75
|
syl2anc |
|
77 |
20
|
nncnd |
|
78 |
23
|
nncnd |
|
79 |
|
1cnd |
|
80 |
77 78 79
|
addsubassd |
|
81 |
|
ax-1cn |
|
82 |
|
npcan |
|
83 |
77 81 82
|
sylancl |
|
84 |
83
|
fveq2d |
|
85 |
76 80 84
|
3eltr4d |
|
86 |
45
|
ffvelrnda |
|
87 |
70 72 85 49 86
|
seqsplit |
|
88 |
|
simpll2 |
|
89 |
|
simpll3 |
|
90 |
53
|
eleq2d |
|
91 |
90
|
biimpar |
|
92 |
|
ccatval1 |
|
93 |
88 89 91 92
|
syl3anc |
|
94 |
49 93
|
seqfveq |
|
95 |
77
|
addid2d |
|
96 |
83 95
|
eqtr4d |
|
97 |
96
|
seqeq1d |
|
98 |
77 78
|
addcomd |
|
99 |
98
|
oveq1d |
|
100 |
78 77 79
|
addsubd |
|
101 |
99 100
|
eqtrd |
|
102 |
97 101
|
fveq12d |
|
103 |
|
simpll2 |
|
104 |
|
simpll3 |
|
105 |
63
|
eleq2d |
|
106 |
105
|
biimpar |
|
107 |
|
ccatval3 |
|
108 |
103 104 106 107
|
syl3anc |
|
109 |
108
|
eqcomd |
|
110 |
59 38 109
|
seqshft2 |
|
111 |
102 110
|
eqtr4d |
|
112 |
94 111
|
oveq12d |
|
113 |
87 112
|
eqtrd |
|
114 |
67 113
|
eqtr4d |
|
115 |
46 114
|
eqtr4d |
|
116 |
115
|
anassrs |
|
117 |
|
simpl2 |
|
118 |
|
ccatrid |
|
119 |
117 118
|
syl |
|
120 |
119
|
oveq2d |
|
121 |
|
simpl1 |
|
122 |
1
|
gsumwcl |
|
123 |
122
|
3adant3 |
|
124 |
123
|
adantr |
|
125 |
1 2 6
|
mndrid |
|
126 |
121 124 125
|
syl2anc |
|
127 |
120 126
|
eqtr4d |
|
128 |
16 116 127
|
pm2.61ne |
|
129 |
|
ccatlid |
|
130 |
129
|
3ad2ant3 |
|
131 |
130
|
oveq2d |
|
132 |
|
simp1 |
|
133 |
1
|
gsumwcl |
|
134 |
1 2 6
|
mndlid |
|
135 |
132 133 134
|
3imp3i2an |
|
136 |
131 135
|
eqtr4d |
|
137 |
10 128 136
|
pm2.61ne |
|