| Step |
Hyp |
Ref |
Expression |
| 1 |
|
gsumwrd2dccatlem.u |
|
| 2 |
|
gsumwrd2dccatlem.f |
|
| 3 |
|
gsumwrd2dccatlem.g |
|
| 4 |
|
gsumwrd2dccatlem.a |
|
| 5 |
|
sneq |
|
| 6 |
|
fveq2 |
|
| 7 |
6
|
oveq2d |
|
| 8 |
5 7
|
xpeq12d |
|
| 9 |
8
|
eleq2d |
|
| 10 |
|
xp1st |
|
| 11 |
10
|
adantl |
|
| 12 |
|
xp2nd |
|
| 13 |
12
|
adantl |
|
| 14 |
|
ccatcl |
|
| 15 |
11 13 14
|
syl2anc |
|
| 16 |
|
ovex |
|
| 17 |
16
|
snid |
|
| 18 |
17
|
a1i |
|
| 19 |
|
0zd |
|
| 20 |
|
lencl |
|
| 21 |
15 20
|
syl |
|
| 22 |
21
|
nn0zd |
|
| 23 |
|
lencl |
|
| 24 |
11 23
|
syl |
|
| 25 |
24
|
nn0zd |
|
| 26 |
24
|
nn0ge0d |
|
| 27 |
|
lencl |
|
| 28 |
13 27
|
syl |
|
| 29 |
28
|
nn0ge0d |
|
| 30 |
24
|
nn0red |
|
| 31 |
28
|
nn0red |
|
| 32 |
30 31
|
addge01d |
|
| 33 |
29 32
|
mpbid |
|
| 34 |
|
ccatlen |
|
| 35 |
11 13 34
|
syl2anc |
|
| 36 |
33 35
|
breqtrrd |
|
| 37 |
19 22 25 26 36
|
elfzd |
|
| 38 |
18 37
|
opelxpd |
|
| 39 |
9 15 38
|
rspcedvdw |
|
| 40 |
39
|
eliund |
|
| 41 |
40 1
|
eleqtrrdi |
|
| 42 |
|
simpr |
|
| 43 |
|
xp1st |
|
| 44 |
|
elsni |
|
| 45 |
42 43 44
|
3syl |
|
| 46 |
|
simplr |
|
| 47 |
45 46
|
eqeltrd |
|
| 48 |
47
|
adantllr |
|
| 49 |
1
|
eleq2i |
|
| 50 |
49
|
biimpi |
|
| 51 |
50
|
adantl |
|
| 52 |
|
eliun |
|
| 53 |
51 52
|
sylib |
|
| 54 |
|
sneq |
|
| 55 |
|
fveq2 |
|
| 56 |
55
|
oveq2d |
|
| 57 |
54 56
|
xpeq12d |
|
| 58 |
57
|
eleq2d |
|
| 59 |
58
|
cbvrexvw |
|
| 60 |
53 59
|
sylibr |
|
| 61 |
48 60
|
r19.29a |
|
| 62 |
|
pfxcl |
|
| 63 |
61 62
|
syl |
|
| 64 |
|
swrdcl |
|
| 65 |
61 64
|
syl |
|
| 66 |
63 65
|
opelxpd |
|
| 67 |
51
|
adantr |
|
| 68 |
|
eliunxp |
|
| 69 |
67 68
|
sylib |
|
| 70 |
|
opeq1 |
|
| 71 |
70
|
eqeq2d |
|
| 72 |
|
eleq1w |
|
| 73 |
56
|
eleq2d |
|
| 74 |
72 73
|
anbi12d |
|
| 75 |
71 74
|
anbi12d |
|
| 76 |
75
|
exbidv |
|
| 77 |
76
|
cbvexvw |
|
| 78 |
69 77
|
sylibr |
|
| 79 |
|
simplr |
|
| 80 |
|
simpr |
|
| 81 |
79 80
|
oveq12d |
|
| 82 |
|
vex |
|
| 83 |
|
vex |
|
| 84 |
82 83
|
op1std |
|
| 85 |
84
|
ad5antlr |
|
| 86 |
|
simp-4r |
|
| 87 |
85 86
|
eqeltrd |
|
| 88 |
82 83
|
op2ndd |
|
| 89 |
88
|
ad5antlr |
|
| 90 |
|
simpllr |
|
| 91 |
85
|
eqcomd |
|
| 92 |
91
|
fveq2d |
|
| 93 |
92
|
oveq2d |
|
| 94 |
90 93
|
eleqtrd |
|
| 95 |
89 94
|
eqeltrd |
|
| 96 |
|
pfxcctswrd |
|
| 97 |
87 95 96
|
syl2anc |
|
| 98 |
81 97
|
eqtr2d |
|
| 99 |
79
|
fveq2d |
|
| 100 |
|
pfxlen |
|
| 101 |
87 95 100
|
syl2anc |
|
| 102 |
99 101
|
eqtr2d |
|
| 103 |
98 102
|
jca |
|
| 104 |
103
|
anasss |
|
| 105 |
|
simplr |
|
| 106 |
|
simpr |
|
| 107 |
105 106
|
oveq12d |
|
| 108 |
11
|
ad5antr |
|
| 109 |
13
|
ad5antr |
|
| 110 |
|
pfxccat1 |
|
| 111 |
108 109 110
|
syl2anc |
|
| 112 |
107 111
|
eqtr2d |
|
| 113 |
105
|
fveq2d |
|
| 114 |
108 109 34
|
syl2anc |
|
| 115 |
113 114
|
eqtrd |
|
| 116 |
106 115
|
opeq12d |
|
| 117 |
105 116
|
oveq12d |
|
| 118 |
|
swrdccat2 |
|
| 119 |
108 109 118
|
syl2anc |
|
| 120 |
117 119
|
eqtr2d |
|
| 121 |
112 120
|
jca |
|
| 122 |
121
|
anasss |
|
| 123 |
104 122
|
impbida |
|
| 124 |
123
|
anasss |
|
| 125 |
124
|
expl |
|
| 126 |
125
|
adantlr |
|
| 127 |
126
|
exlimdv |
|
| 128 |
127
|
imp |
|
| 129 |
78 128
|
exlimddv |
|
| 130 |
|
eqop |
|
| 131 |
130
|
adantl |
|
| 132 |
|
snssi |
|
| 133 |
132
|
adantl |
|
| 134 |
|
fz0ssnn0 |
|
| 135 |
|
xpss12 |
|
| 136 |
133 134 135
|
sylancl |
|
| 137 |
136
|
iunssd |
|
| 138 |
137
|
adantlr |
|
| 139 |
138 67
|
sseldd |
|
| 140 |
|
eqop |
|
| 141 |
139 140
|
syl |
|
| 142 |
129 131 141
|
3bitr4d |
|
| 143 |
142
|
an32s |
|
| 144 |
143
|
anasss |
|
| 145 |
2 41 66 144
|
f1ocnv2d |
|
| 146 |
145
|
simpld |
|
| 147 |
145
|
simprd |
|
| 148 |
147 3
|
eqtr4di |
|
| 149 |
146 148
|
jca |
|