Step |
Hyp |
Ref |
Expression |
1 |
|
dyadmbl.1 |
|
2 |
|
simplll |
|
3 |
|
simplrl |
|
4 |
1
|
dyadval |
|
5 |
2 3 4
|
syl2anc |
|
6 |
5
|
fveq2d |
|
7 |
|
df-ov |
|
8 |
6 7
|
eqtr4di |
|
9 |
|
simpllr |
|
10 |
|
simplrr |
|
11 |
1
|
dyadval |
|
12 |
9 10 11
|
syl2anc |
|
13 |
12
|
fveq2d |
|
14 |
|
df-ov |
|
15 |
13 14
|
eqtr4di |
|
16 |
8 15
|
ineq12d |
|
17 |
|
incom |
|
18 |
16 17
|
eqtrdi |
|
19 |
18
|
adantr |
|
20 |
2
|
zred |
|
21 |
20
|
recnd |
|
22 |
|
2nn |
|
23 |
|
nnexpcl |
|
24 |
22 3 23
|
sylancr |
|
25 |
24
|
nncnd |
|
26 |
|
nnexpcl |
|
27 |
22 10 26
|
sylancr |
|
28 |
27
|
nncnd |
|
29 |
24
|
nnne0d |
|
30 |
21 25 28 29
|
div13d |
|
31 |
|
2cnd |
|
32 |
|
2ne0 |
|
33 |
32
|
a1i |
|
34 |
3
|
nn0zd |
|
35 |
10
|
nn0zd |
|
36 |
31 33 34 35
|
expsubd |
|
37 |
|
2z |
|
38 |
|
simpr |
|
39 |
|
znn0sub |
|
40 |
34 35 39
|
syl2anc |
|
41 |
38 40
|
mpbid |
|
42 |
|
zexpcl |
|
43 |
37 41 42
|
sylancr |
|
44 |
36 43
|
eqeltrrd |
|
45 |
44 2
|
zmulcld |
|
46 |
30 45
|
eqeltrd |
|
47 |
|
zltp1le |
|
48 |
9 46 47
|
syl2anc |
|
49 |
9
|
zred |
|
50 |
20 24
|
nndivred |
|
51 |
27
|
nnred |
|
52 |
27
|
nngt0d |
|
53 |
|
ltdivmul2 |
|
54 |
49 50 51 52 53
|
syl112anc |
|
55 |
|
peano2re |
|
56 |
49 55
|
syl |
|
57 |
|
ledivmul2 |
|
58 |
56 50 51 52 57
|
syl112anc |
|
59 |
48 54 58
|
3bitr4d |
|
60 |
49 27
|
nndivred |
|
61 |
60
|
rexrd |
|
62 |
56 27
|
nndivred |
|
63 |
62
|
rexrd |
|
64 |
50
|
rexrd |
|
65 |
|
peano2re |
|
66 |
20 65
|
syl |
|
67 |
66 24
|
nndivred |
|
68 |
67
|
rexrd |
|
69 |
|
ioodisj |
|
70 |
69
|
ex |
|
71 |
61 63 64 68 70
|
syl22anc |
|
72 |
59 71
|
sylbid |
|
73 |
72
|
imp |
|
74 |
19 73
|
eqtrd |
|
75 |
74
|
3mix3d |
|
76 |
50
|
adantr |
|
77 |
67
|
adantr |
|
78 |
|
simprl |
|
79 |
66
|
recnd |
|
80 |
79 25 28 29
|
div13d |
|
81 |
2
|
peano2zd |
|
82 |
44 81
|
zmulcld |
|
83 |
80 82
|
eqeltrd |
|
84 |
|
zltp1le |
|
85 |
9 83 84
|
syl2anc |
|
86 |
|
ltdivmul2 |
|
87 |
49 67 51 52 86
|
syl112anc |
|
88 |
|
ledivmul2 |
|
89 |
56 67 51 52 88
|
syl112anc |
|
90 |
85 87 89
|
3bitr4d |
|
91 |
90
|
biimpa |
|
92 |
91
|
adantrl |
|
93 |
|
iccss |
|
94 |
76 77 78 92 93
|
syl22anc |
|
95 |
12
|
fveq2d |
|
96 |
|
df-ov |
|
97 |
95 96
|
eqtr4di |
|
98 |
97
|
adantr |
|
99 |
5
|
fveq2d |
|
100 |
|
df-ov |
|
101 |
99 100
|
eqtr4di |
|
102 |
101
|
adantr |
|
103 |
94 98 102
|
3sstr4d |
|
104 |
103
|
3mix2d |
|
105 |
104
|
anassrs |
|
106 |
16
|
adantr |
|
107 |
|
ioodisj |
|
108 |
107
|
ex |
|
109 |
64 68 61 63 108
|
syl22anc |
|
110 |
109
|
imp |
|
111 |
106 110
|
eqtrd |
|
112 |
111
|
3mix3d |
|
113 |
112
|
adantlr |
|
114 |
60
|
adantr |
|
115 |
67
|
adantr |
|
116 |
105 113 114 115
|
ltlecasei |
|
117 |
75 116 60 50
|
ltlecasei |
|