Step |
Hyp |
Ref |
Expression |
1 |
|
rusgrnumwwlk.v |
|
2 |
|
rusgrnumwwlk.l |
|
3 |
|
simpr2 |
|
4 |
|
simpr3 |
|
5 |
1 2
|
rusgrnumwwlklem |
|
6 |
5
|
eqeq1d |
|
7 |
3 4 6
|
syl2anc |
|
8 |
|
eqid |
|
9 |
8
|
wwlksnredwwlkn0 |
|
10 |
9
|
ex |
|
11 |
10
|
3ad2ant3 |
|
12 |
11
|
adantl |
|
13 |
12
|
imp |
|
14 |
13
|
rabbidva |
|
15 |
14
|
adantr |
|
16 |
15
|
fveq2d |
|
17 |
|
simp2 |
|
18 |
17
|
pm4.71ri |
|
19 |
18
|
a1i |
|
20 |
19
|
rexbidva |
|
21 |
|
fveq1 |
|
22 |
21
|
eqeq1d |
|
23 |
22
|
rexrab |
|
24 |
20 23
|
bitr4di |
|
25 |
24
|
rabbidva |
|
26 |
25
|
adantr |
|
27 |
26
|
fveq2d |
|
28 |
|
simplr1 |
|
29 |
1
|
eleq1i |
|
30 |
29
|
biimpi |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
31 8 32
|
hashwwlksnext |
|
34 |
28 30 33
|
3syl |
|
35 |
|
fveq1 |
|
36 |
35
|
eqeq1d |
|
37 |
36
|
cbvrabv |
|
38 |
37
|
sumeq1i |
|
39 |
38
|
a1i |
|
40 |
27 34 39
|
3eqtrd |
|
41 |
|
rusgrnumwwlkslem |
|
42 |
41
|
eqcomd |
|
43 |
42
|
fveq2d |
|
44 |
43
|
adantl |
|
45 |
|
elrabi |
|
46 |
45
|
adantl |
|
47 |
1 8
|
wwlksnexthasheq |
|
48 |
46 47
|
syl |
|
49 |
1
|
rusgrpropadjvtx |
|
50 |
|
fveq1 |
|
51 |
50
|
eqeq1d |
|
52 |
51
|
elrab |
|
53 |
1 8
|
wwlknp |
|
54 |
53
|
adantr |
|
55 |
|
simpll |
|
56 |
|
nn0p1gt0 |
|
57 |
56
|
3ad2ant3 |
|
58 |
57
|
adantl |
|
59 |
|
breq2 |
|
60 |
59
|
ad2antlr |
|
61 |
58 60
|
mpbird |
|
62 |
|
hashle00 |
|
63 |
|
lencl |
|
64 |
63
|
nn0red |
|
65 |
|
0re |
|
66 |
|
lenlt |
|
67 |
66
|
bicomd |
|
68 |
64 65 67
|
sylancl |
|
69 |
|
nne |
|
70 |
69
|
a1i |
|
71 |
62 68 70
|
3bitr4rd |
|
72 |
71
|
ad2antrr |
|
73 |
72
|
con4bid |
|
74 |
61 73
|
mpbird |
|
75 |
55 74
|
jca |
|
76 |
75
|
ex |
|
77 |
76
|
3adant3 |
|
78 |
54 77
|
syl |
|
79 |
52 78
|
sylbi |
|
80 |
79
|
imp |
|
81 |
|
lswcl |
|
82 |
80 81
|
syl |
|
83 |
82
|
ad2antrr |
|
84 |
|
preq1 |
|
85 |
84
|
eleq1d |
|
86 |
85
|
rabbidv |
|
87 |
86
|
fveqeq2d |
|
88 |
87
|
rspcva |
|
89 |
83 88
|
sylancom |
|
90 |
89
|
exp41 |
|
91 |
90
|
com14 |
|
92 |
91
|
3ad2ant3 |
|
93 |
49 92
|
syl |
|
94 |
93
|
imp41 |
|
95 |
44 48 94
|
3eqtrd |
|
96 |
95
|
sumeq2dv |
|
97 |
|
oveq1 |
|
98 |
97
|
adantl |
|
99 |
|
wwlksnfi |
|
100 |
29 99
|
sylbi |
|
101 |
100
|
3ad2ant1 |
|
102 |
101
|
ad2antlr |
|
103 |
|
rabfi |
|
104 |
102 103
|
syl |
|
105 |
|
rusgrusgr |
|
106 |
|
simp1 |
|
107 |
105 106
|
anim12i |
|
108 |
1
|
isfusgr |
|
109 |
107 108
|
sylibr |
|
110 |
|
simpl |
|
111 |
|
ne0i |
|
112 |
111
|
3ad2ant2 |
|
113 |
112
|
adantl |
|
114 |
1
|
frusgrnn0 |
|
115 |
109 110 113 114
|
syl3anc |
|
116 |
115
|
nn0cnd |
|
117 |
116
|
adantr |
|
118 |
|
fsumconst |
|
119 |
104 117 118
|
syl2anc |
|
120 |
116 4
|
expp1d |
|
121 |
120
|
adantr |
|
122 |
98 119 121
|
3eqtr4d |
|
123 |
96 122
|
eqtrd |
|
124 |
16 40 123
|
3eqtrd |
|
125 |
|
peano2nn0 |
|
126 |
125
|
3ad2ant3 |
|
127 |
126
|
adantl |
|
128 |
1 2
|
rusgrnumwwlklem |
|
129 |
128
|
eqeq1d |
|
130 |
3 127 129
|
syl2anc |
|
131 |
130
|
adantr |
|
132 |
124 131
|
mpbird |
|
133 |
132
|
ex |
|
134 |
7 133
|
sylbid |
|