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 |
|