Step |
Hyp |
Ref |
Expression |
1 |
|
wwlksnext.v |
|
2 |
|
wwlksnext.e |
|
3 |
1
|
wwlknbp |
|
4 |
1 2
|
wwlknp |
|
5 |
|
simp1 |
|
6 |
|
simprl |
|
7 |
|
cats1un |
|
8 |
5 6 7
|
syl2an |
|
9 |
|
opex |
|
10 |
9
|
snnz |
|
11 |
10
|
neii |
|
12 |
11
|
intnan |
|
13 |
|
df-ne |
|
14 |
|
un00 |
|
15 |
13 14
|
xchbinxr |
|
16 |
12 15
|
mpbir |
|
17 |
16
|
a1i |
|
18 |
8 17
|
eqnetrd |
|
19 |
|
s1cl |
|
20 |
19
|
ad2antrl |
|
21 |
|
ccatcl |
|
22 |
5 20 21
|
syl2an |
|
23 |
|
simplrl |
|
24 |
|
fzossfzop1 |
|
25 |
24
|
ad2antrr |
|
26 |
25
|
sselda |
|
27 |
|
oveq2 |
|
28 |
27
|
eleq2d |
|
29 |
28
|
adantl |
|
30 |
29
|
ad2antlr |
|
31 |
26 30
|
mpbird |
|
32 |
|
ccats1val1 |
|
33 |
23 31 32
|
syl2anc |
|
34 |
|
fzonn0p1p1 |
|
35 |
34
|
adantl |
|
36 |
27
|
adantl |
|
37 |
36
|
ad2antlr |
|
38 |
35 37
|
eleqtrrd |
|
39 |
|
ccats1val1 |
|
40 |
23 38 39
|
syl2anc |
|
41 |
33 40
|
preq12d |
|
42 |
41
|
exp31 |
|
43 |
42
|
adantrr |
|
44 |
43
|
impcom |
|
45 |
44
|
imp |
|
46 |
45
|
eleq1d |
|
47 |
46
|
ralbidva |
|
48 |
47
|
exbiri |
|
49 |
48
|
com23 |
|
50 |
49
|
3impia |
|
51 |
50
|
imp |
|
52 |
|
oveq1 |
|
53 |
52
|
adantl |
|
54 |
|
nn0cn |
|
55 |
|
1cnd |
|
56 |
54 55
|
pncand |
|
57 |
56
|
adantl |
|
58 |
53 57
|
sylan9eqr |
|
59 |
58
|
fveq2d |
|
60 |
|
lsw |
|
61 |
60
|
ad2antrl |
|
62 |
|
simprl |
|
63 |
|
fzonn0p1 |
|
64 |
63
|
ad2antlr |
|
65 |
27
|
eleq2d |
|
66 |
65
|
ad2antll |
|
67 |
64 66
|
mpbird |
|
68 |
|
ccats1val1 |
|
69 |
62 67 68
|
syl2anc |
|
70 |
59 61 69
|
3eqtr4d |
|
71 |
|
simpll |
|
72 |
|
simprr |
|
73 |
72
|
eqcomd |
|
74 |
|
ccats1val2 |
|
75 |
74
|
eqcomd |
|
76 |
62 71 73 75
|
syl3anc |
|
77 |
70 76
|
preq12d |
|
78 |
77
|
eleq1d |
|
79 |
78
|
biimpcd |
|
80 |
79
|
exp4c |
|
81 |
80
|
impcom |
|
82 |
81
|
impcom |
|
83 |
82
|
impcom |
|
84 |
83
|
3adantl3 |
|
85 |
|
fveq2 |
|
86 |
|
fvoveq1 |
|
87 |
85 86
|
preq12d |
|
88 |
87
|
eleq1d |
|
89 |
88
|
ralsng |
|
90 |
89
|
ad2antrl |
|
91 |
84 90
|
mpbird |
|
92 |
|
ralunb |
|
93 |
51 91 92
|
sylanbrc |
|
94 |
|
elnn0uz |
|
95 |
|
eluzfz2 |
|
96 |
94 95
|
sylbi |
|
97 |
|
fzelp1 |
|
98 |
|
fzosplit |
|
99 |
96 97 98
|
3syl |
|
100 |
|
nn0z |
|
101 |
|
fzosn |
|
102 |
100 101
|
syl |
|
103 |
102
|
uneq2d |
|
104 |
99 103
|
eqtrd |
|
105 |
104
|
ad2antrl |
|
106 |
105
|
raleqdv |
|
107 |
93 106
|
mpbird |
|
108 |
|
ccatlen |
|
109 |
5 20 108
|
syl2an |
|
110 |
109
|
oveq1d |
|
111 |
|
simpl2 |
|
112 |
|
s1len |
|
113 |
112
|
a1i |
|
114 |
111 113
|
oveq12d |
|
115 |
114
|
oveq1d |
|
116 |
|
peano2nn0 |
|
117 |
116
|
nn0cnd |
|
118 |
117 55
|
pncand |
|
119 |
118
|
ad2antrl |
|
120 |
110 115 119
|
3eqtrd |
|
121 |
120
|
oveq2d |
|
122 |
121
|
raleqdv |
|
123 |
107 122
|
mpbird |
|
124 |
18 22 123
|
3jca |
|
125 |
109 114
|
eqtrd |
|
126 |
124 125
|
jca |
|
127 |
126
|
ex |
|
128 |
4 127
|
syl |
|
129 |
128
|
expd |
|
130 |
129
|
impcom |
|
131 |
130
|
adantll |
|
132 |
|
iswwlksn |
|
133 |
116 132
|
syl |
|
134 |
133
|
adantl |
|
135 |
1 2
|
iswwlks |
|
136 |
135
|
anbi1i |
|
137 |
134 136
|
syl6bb |
|
138 |
137
|
adantr |
|
139 |
131 138
|
sylibrd |
|
140 |
139
|
ex |
|
141 |
140
|
3adant3 |
|
142 |
3 141
|
mpcom |
|
143 |
142
|
3impib |
|