Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem10.1 |
|
2 |
|
lcmineqlem10.2 |
|
3 |
|
lcmineqlem10.3 |
|
4 |
2
|
nncnd |
|
5 |
1
|
nncnd |
|
6 |
4 5
|
subcld |
|
7 |
|
elunitcn |
|
8 |
1
|
nnnn0d |
|
9 |
|
expcl |
|
10 |
8 9
|
sylan2 |
|
11 |
10
|
ancoms |
|
12 |
7 11
|
sylan2 |
|
13 |
|
1cnd |
|
14 |
|
simpr |
|
15 |
13 14
|
subcld |
|
16 |
1
|
nnzd |
|
17 |
2
|
nnzd |
|
18 |
|
znnsub |
|
19 |
16 17 18
|
syl2anc |
|
20 |
3 19
|
mpbid |
|
21 |
|
nnm1nn0 |
|
22 |
20 21
|
syl |
|
23 |
22
|
adantr |
|
24 |
15 23
|
expcld |
|
25 |
7 24
|
sylan2 |
|
26 |
12 25
|
mulcld |
|
27 |
|
0red |
|
28 |
|
1red |
|
29 |
|
expcncf |
|
30 |
8 29
|
syl |
|
31 |
|
1nn |
|
32 |
31
|
a1i |
|
33 |
20
|
nnge1d |
|
34 |
32 20 33
|
lcmineqlem9 |
|
35 |
30 34
|
mulcncf |
|
36 |
35
|
resclunitintvd |
|
37 |
|
cnicciblnc |
|
38 |
27 28 36 37
|
syl3anc |
|
39 |
26 38
|
itgcl |
|
40 |
6 39
|
mulneg1d |
|
41 |
6
|
negcld |
|
42 |
41 26 38
|
itgmulc2 |
|
43 |
4
|
adantr |
|
44 |
5
|
adantr |
|
45 |
43 44
|
subcld |
|
46 |
45
|
negcld |
|
47 |
11 46 24
|
mul12d |
|
48 |
7 47
|
sylan2 |
|
49 |
48
|
itgeq2dv |
|
50 |
4
|
adantr |
|
51 |
5
|
adantr |
|
52 |
50 51
|
subcld |
|
53 |
52
|
negcld |
|
54 |
53 25
|
mulcld |
|
55 |
12 54
|
mulcld |
|
56 |
27 28 55
|
itgioo |
|
57 |
|
0le1 |
|
58 |
57
|
a1i |
|
59 |
30
|
resclunitintvd |
|
60 |
1
|
nnred |
|
61 |
2
|
nnred |
|
62 |
|
ltle |
|
63 |
60 61 62
|
syl2anc |
|
64 |
3 63
|
mpd |
|
65 |
1 2 64
|
lcmineqlem9 |
|
66 |
65
|
resclunitintvd |
|
67 |
|
ssid |
|
68 |
|
cncfmptc |
|
69 |
67 67 68
|
mp3an23 |
|
70 |
5 69
|
syl |
|
71 |
70
|
resopunitintvd |
|
72 |
|
nnm1nn0 |
|
73 |
|
expcncf |
|
74 |
1 72 73
|
3syl |
|
75 |
74
|
resopunitintvd |
|
76 |
71 75
|
mulcncf |
|
77 |
|
cncfmptc |
|
78 |
67 67 77
|
mp3an23 |
|
79 |
41 78
|
syl |
|
80 |
79
|
resopunitintvd |
|
81 |
34
|
resopunitintvd |
|
82 |
80 81
|
mulcncf |
|
83 |
|
ioossicc |
|
84 |
83
|
a1i |
|
85 |
|
ioombl |
|
86 |
85
|
a1i |
|
87 |
79 34
|
mulcncf |
|
88 |
30 87
|
mulcncf |
|
89 |
88
|
resclunitintvd |
|
90 |
|
cnicciblnc |
|
91 |
27 28 89 90
|
syl3anc |
|
92 |
84 86 55 91
|
iblss |
|
93 |
1 72
|
syl |
|
94 |
|
expcl |
|
95 |
93 94
|
sylan2 |
|
96 |
95
|
ancoms |
|
97 |
7 96
|
sylan2 |
|
98 |
51 97
|
mulcld |
|
99 |
20
|
nnnn0d |
|
100 |
99
|
adantr |
|
101 |
15 100
|
expcld |
|
102 |
7 101
|
sylan2 |
|
103 |
98 102
|
mulcld |
|
104 |
70 74
|
mulcncf |
|
105 |
104 65
|
mulcncf |
|
106 |
105
|
resclunitintvd |
|
107 |
|
cnicciblnc |
|
108 |
27 28 106 107
|
syl3anc |
|
109 |
84 86 103 108
|
iblss |
|
110 |
|
dvexp |
|
111 |
1 110
|
syl |
|
112 |
44 96
|
mulcld |
|
113 |
111 11 112
|
resdvopclptsd |
|
114 |
1 2 3
|
lcmineqlem8 |
|
115 |
46 24
|
mulcld |
|
116 |
114 101 115
|
resdvopclptsd |
|
117 |
|
oveq1 |
|
118 |
117
|
adantl |
|
119 |
1
|
0expd |
|
120 |
119
|
adantr |
|
121 |
118 120
|
eqtrd |
|
122 |
121
|
oveq1d |
|
123 |
|
0cn |
|
124 |
|
eleq1 |
|
125 |
123 124
|
mpbiri |
|
126 |
101
|
mul02d |
|
127 |
125 126
|
sylan2 |
|
128 |
122 127
|
eqtrd |
|
129 |
|
oveq2 |
|
130 |
|
1m1e0 |
|
131 |
129 130
|
eqtrdi |
|
132 |
131
|
oveq1d |
|
133 |
132
|
adantl |
|
134 |
20
|
0expd |
|
135 |
134
|
adantr |
|
136 |
133 135
|
eqtrd |
|
137 |
136
|
oveq2d |
|
138 |
|
ax-1cn |
|
139 |
|
eleq1 |
|
140 |
138 139
|
mpbiri |
|
141 |
11
|
mul01d |
|
142 |
140 141
|
sylan2 |
|
143 |
137 142
|
eqtrd |
|
144 |
27 28 58 59 66 76 82 92 109 113 116 128 143
|
itgparts |
|
145 |
56 144
|
eqtr3d |
|
146 |
27 28 103
|
itgioo |
|
147 |
146
|
oveq2d |
|
148 |
145 147
|
eqtrd |
|
149 |
|
0m0e0 |
|
150 |
149
|
oveq1i |
|
151 |
148 150
|
eqtrdi |
|
152 |
49 151
|
eqtr3d |
|
153 |
42 152
|
eqtrd |
|
154 |
44 96 101
|
mulassd |
|
155 |
7 154
|
sylan2 |
|
156 |
155
|
itgeq2dv |
|
157 |
156
|
oveq2d |
|
158 |
153 157
|
eqtrd |
|
159 |
97 102
|
mulcld |
|
160 |
74 65
|
mulcncf |
|
161 |
160
|
resclunitintvd |
|
162 |
|
cnicciblnc |
|
163 |
27 28 161 162
|
syl3anc |
|
164 |
5 159 163
|
itgmulc2 |
|
165 |
164
|
oveq2d |
|
166 |
158 165
|
eqtr4d |
|
167 |
|
df-neg |
|
168 |
166 167
|
eqtr4di |
|
169 |
40 168
|
eqtr3d |
|
170 |
6 39
|
mulcld |
|
171 |
159 163
|
itgcl |
|
172 |
5 171
|
mulcld |
|
173 |
170 172
|
neg11ad |
|
174 |
169 173
|
mpbid |
|
175 |
20
|
nnne0d |
|
176 |
172 6 39 175
|
divmuld |
|
177 |
174 176
|
mpbird |
|
178 |
138
|
a1i |
|
179 |
5 178
|
pncand |
|
180 |
179
|
eqcomd |
|
181 |
180
|
oveq2d |
|
182 |
4 5 178
|
subsub4d |
|
183 |
182
|
oveq2d |
|
184 |
181 183
|
oveq12d |
|
185 |
184
|
adantr |
|
186 |
185
|
itgeq2dv |
|
187 |
177 186
|
eqtrd |
|
188 |
187
|
eqcomd |
|
189 |
5 171 6 175
|
div23d |
|
190 |
188 189
|
eqtrd |
|