Step |
Hyp |
Ref |
Expression |
1 |
|
zre |
|
2 |
1
|
3ad2ant1 |
|
3 |
|
2rp |
|
4 |
3
|
a1i |
|
5 |
|
nnz |
|
6 |
4 5
|
rpexpcld |
|
7 |
6
|
rpred |
|
8 |
7
|
3ad2ant3 |
|
9 |
2 8
|
resubcld |
|
10 |
6
|
3ad2ant3 |
|
11 |
9 10
|
modcld |
|
12 |
9 11
|
resubcld |
|
13 |
|
peano2zm |
|
14 |
13
|
zred |
|
15 |
14
|
3ad2ant1 |
|
16 |
15 10
|
modcld |
|
17 |
15 16
|
resubcld |
|
18 |
|
1red |
|
19 |
18 16
|
readdcld |
|
20 |
8 11
|
readdcld |
|
21 |
|
2nn |
|
22 |
21
|
a1i |
|
23 |
|
nnnn0 |
|
24 |
22 23
|
nnexpcld |
|
25 |
24
|
anim2i |
|
26 |
25
|
3adant2 |
|
27 |
|
m1modmmod |
|
28 |
26 27
|
syl |
|
29 |
|
nnz |
|
30 |
29
|
a1i |
|
31 |
|
zcn |
|
32 |
|
xp1d2m1eqxm1d2 |
|
33 |
32
|
eqcomd |
|
34 |
31 33
|
syl |
|
35 |
34
|
adantr |
|
36 |
35
|
eleq1d |
|
37 |
|
peano2z |
|
38 |
31
|
adantr |
|
39 |
|
1cnd |
|
40 |
38 39
|
addcld |
|
41 |
40
|
halfcld |
|
42 |
41 39
|
npcand |
|
43 |
42
|
eleq1d |
|
44 |
37 43
|
syl5ib |
|
45 |
36 44
|
sylbid |
|
46 |
|
mod0 |
|
47 |
1 6 46
|
syl2an |
|
48 |
22
|
nnzd |
|
49 |
|
nnm1nn0 |
|
50 |
|
zexpcl |
|
51 |
48 49 50
|
syl2anc |
|
52 |
51
|
adantl |
|
53 |
52
|
adantr |
|
54 |
|
simpr |
|
55 |
53 54
|
zmulcld |
|
56 |
55
|
ex |
|
57 |
5
|
adantl |
|
58 |
57
|
zcnd |
|
59 |
39
|
negcld |
|
60 |
58 39
|
negsubd |
|
61 |
60
|
eqcomd |
|
62 |
58 59 61
|
mvrladdd |
|
63 |
62
|
oveq2d |
|
64 |
|
2cnd |
|
65 |
|
2ne0 |
|
66 |
65
|
a1i |
|
67 |
|
1zzd |
|
68 |
5 67
|
zsubcld |
|
69 |
68 5
|
jca |
|
70 |
69
|
adantl |
|
71 |
|
expsub |
|
72 |
64 66 70 71
|
syl21anc |
|
73 |
|
expn1 |
|
74 |
64 73
|
syl |
|
75 |
63 72 74
|
3eqtr3d |
|
76 |
75
|
oveq2d |
|
77 |
|
2cnd |
|
78 |
77 49
|
expcld |
|
79 |
78
|
adantl |
|
80 |
3
|
a1i |
|
81 |
80 57
|
rpexpcld |
|
82 |
81
|
rpcnne0d |
|
83 |
|
div12 |
|
84 |
79 38 82 83
|
syl3anc |
|
85 |
38 64 66
|
divrecd |
|
86 |
76 84 85
|
3eqtr4d |
|
87 |
86
|
eleq1d |
|
88 |
56 87
|
sylibd |
|
89 |
47 88
|
sylbid |
|
90 |
|
zeo2 |
|
91 |
90
|
adantr |
|
92 |
89 91
|
sylibd |
|
93 |
92
|
necon2ad |
|
94 |
30 45 93
|
3syld |
|
95 |
94
|
ex |
|
96 |
95
|
com23 |
|
97 |
96
|
3imp |
|
98 |
97
|
neneqd |
|
99 |
98
|
iffalsed |
|
100 |
28 99
|
eqtrd |
|
101 |
|
neg1lt0 |
|
102 |
|
2re |
|
103 |
|
1lt2 |
|
104 |
|
expgt1 |
|
105 |
102 103 104
|
mp3an13 |
|
106 |
|
1red |
|
107 |
106 7
|
posdifd |
|
108 |
105 107
|
mpbid |
|
109 |
106
|
renegcld |
|
110 |
|
0red |
|
111 |
7 106
|
resubcld |
|
112 |
|
lttr |
|
113 |
109 110 111 112
|
syl3anc |
|
114 |
108 113
|
mpan2d |
|
115 |
101 114
|
mpi |
|
116 |
115
|
3ad2ant3 |
|
117 |
100 116
|
eqbrtrd |
|
118 |
2 10
|
modcld |
|
119 |
|
ltsubadd2b |
|
120 |
18 8 118 16 119
|
syl22anc |
|
121 |
117 120
|
mpbid |
|
122 |
|
modid0 |
|
123 |
10 122
|
syl |
|
124 |
123
|
oveq2d |
|
125 |
118
|
recnd |
|
126 |
125
|
subid1d |
|
127 |
124 126
|
eqtrd |
|
128 |
127
|
oveq1d |
|
129 |
|
modsubmodmod |
|
130 |
2 8 10 129
|
syl3anc |
|
131 |
|
modabs2 |
|
132 |
2 10 131
|
syl2anc |
|
133 |
128 130 132
|
3eqtr3d |
|
134 |
133
|
oveq2d |
|
135 |
121 134
|
breqtrrd |
|
136 |
19 20 2 135
|
ltsub2dd |
|
137 |
31
|
3ad2ant1 |
|
138 |
8
|
recnd |
|
139 |
11
|
recnd |
|
140 |
137 138 139
|
subsub4d |
|
141 |
|
1cnd |
|
142 |
16
|
recnd |
|
143 |
137 141 142
|
subsub4d |
|
144 |
136 140 143
|
3brtr4d |
|
145 |
12 17 10 144
|
ltdiv1dd |
|
146 |
7
|
recnd |
|
147 |
146
|
3ad2ant3 |
|
148 |
65
|
a1i |
|
149 |
77 148 5
|
expne0d |
|
150 |
149
|
3ad2ant3 |
|
151 |
|
divsub1dir |
|
152 |
151
|
fveq2d |
|
153 |
137 147 150 152
|
syl3anc |
|
154 |
|
fldivmod |
|
155 |
9 10 154
|
syl2anc |
|
156 |
153 155
|
eqtrd |
|
157 |
|
fldivmod |
|
158 |
15 10 157
|
syl2anc |
|
159 |
145 156 158
|
3brtr4d |
|