Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem12.1 |
|
2 |
|
elunitcn |
|
3 |
|
1m1e0 |
|
4 |
3
|
oveq2i |
|
5 |
|
simpr |
|
6 |
5
|
exp0d |
|
7 |
4 6
|
syl5eq |
|
8 |
7
|
oveq1d |
|
9 |
|
1cnd |
|
10 |
9 5
|
subcld |
|
11 |
|
nnm1nn0 |
|
12 |
1 11
|
syl |
|
13 |
12
|
adantr |
|
14 |
10 13
|
expcld |
|
15 |
14
|
mulid2d |
|
16 |
8 15
|
eqtrd |
|
17 |
2 16
|
sylan2 |
|
18 |
17
|
itgeq2dv |
|
19 |
|
0red |
|
20 |
|
1red |
|
21 |
2 14
|
sylan2 |
|
22 |
19 20 21
|
itgioo |
|
23 |
|
eqidd |
|
24 |
|
oveq2 |
|
25 |
24
|
oveq1d |
|
26 |
25
|
adantl |
|
27 |
26
|
adantlr |
|
28 |
|
simpr |
|
29 |
|
1cnd |
|
30 |
|
elioore |
|
31 |
|
recn |
|
32 |
28 30 31
|
3syl |
|
33 |
29 32
|
subcld |
|
34 |
12
|
adantr |
|
35 |
33 34
|
expcld |
|
36 |
23 27 28 35
|
fvmptd |
|
37 |
36
|
itgeq2dv |
|
38 |
|
cnelprrecn |
|
39 |
38
|
a1i |
|
40 |
|
1cnd |
|
41 |
|
simpr |
|
42 |
40 41
|
subcld |
|
43 |
|
nnnn0 |
|
44 |
1 43
|
syl |
|
45 |
44
|
adantr |
|
46 |
42 45
|
expcld |
|
47 |
45
|
nn0cnd |
|
48 |
12
|
adantr |
|
49 |
42 48
|
expcld |
|
50 |
47 49
|
mulcld |
|
51 |
40
|
negcld |
|
52 |
50 51
|
mulcld |
|
53 |
|
simpr |
|
54 |
44
|
adantr |
|
55 |
53 54
|
expcld |
|
56 |
54
|
nn0cnd |
|
57 |
12
|
adantr |
|
58 |
53 57
|
expcld |
|
59 |
56 58
|
mulcld |
|
60 |
|
0cnd |
|
61 |
|
1cnd |
|
62 |
39 61
|
dvmptc |
|
63 |
39
|
dvmptid |
|
64 |
39 40 60 62 41 40 63
|
dvmptsub |
|
65 |
|
df-neg |
|
66 |
65
|
a1i |
|
67 |
66
|
mpteq2dv |
|
68 |
64 67
|
eqtr4d |
|
69 |
|
dvexp |
|
70 |
1 69
|
syl |
|
71 |
|
oveq1 |
|
72 |
|
oveq1 |
|
73 |
72
|
oveq2d |
|
74 |
39 39 42 51 55 59 68 70 71 73
|
dvmptco |
|
75 |
61
|
negcld |
|
76 |
1
|
nncnd |
|
77 |
1
|
nnne0d |
|
78 |
75 76 77
|
divcld |
|
79 |
39 46 52 74 78
|
dvmptcmul |
|
80 |
78
|
adantr |
|
81 |
80 50 51
|
mulassd |
|
82 |
81
|
eqcomd |
|
83 |
80 47 49
|
mulassd |
|
84 |
83
|
oveq1d |
|
85 |
84
|
eqcomd |
|
86 |
82 85
|
eqtrd |
|
87 |
77
|
adantr |
|
88 |
51 47 87
|
divcan1d |
|
89 |
88
|
oveq1d |
|
90 |
89
|
oveq1d |
|
91 |
86 90
|
eqtrd |
|
92 |
51 51 49
|
mul32d |
|
93 |
92
|
eqcomd |
|
94 |
91 93
|
eqtrd |
|
95 |
40 40
|
mul2negd |
|
96 |
|
1t1e1 |
|
97 |
95 96
|
eqtrdi |
|
98 |
97
|
oveq1d |
|
99 |
49
|
mulid2d |
|
100 |
98 99
|
eqtrd |
|
101 |
94 100
|
eqtrd |
|
102 |
101
|
mpteq2dva |
|
103 |
79 102
|
eqtrd |
|
104 |
80 46
|
mulcld |
|
105 |
103 104 49
|
resdvopclptsd |
|
106 |
105
|
fveq1d |
|
107 |
106
|
ralrimivw |
|
108 |
|
itgeq2 |
|
109 |
107 108
|
syl |
|
110 |
|
0le1 |
|
111 |
110
|
a1i |
|
112 |
|
nfv |
|
113 |
|
ax-1cn |
|
114 |
|
ssid |
|
115 |
|
cncfmptc |
|
116 |
113 114 114 115
|
mp3an |
|
117 |
116
|
a1i |
|
118 |
|
cncfmptid |
|
119 |
114 114 118
|
mp2an |
|
120 |
119
|
a1i |
|
121 |
117 120
|
subcncf |
|
122 |
|
expcncf |
|
123 |
12 122
|
syl |
|
124 |
|
ssidd |
|
125 |
112 121 123 124 72
|
cncfcompt2 |
|
126 |
125
|
resopunitintvd |
|
127 |
105
|
eleq1d |
|
128 |
126 127
|
mpbird |
|
129 |
|
ioossicc |
|
130 |
129
|
a1i |
|
131 |
|
ioombl |
|
132 |
131
|
a1i |
|
133 |
|
elunitcn |
|
134 |
133 49
|
sylan2 |
|
135 |
114
|
a1i |
|
136 |
112 121 123 135 72
|
cncfcompt2 |
|
137 |
136
|
resclunitintvd |
|
138 |
19 20 137
|
3jca |
|
139 |
|
cnicciblnc |
|
140 |
138 139
|
syl |
|
141 |
130 132 134 140
|
iblss |
|
142 |
105 141
|
eqeltrd |
|
143 |
|
cncfmptc |
|
144 |
114 114 143
|
mp3an23 |
|
145 |
78 144
|
syl |
|
146 |
145
|
resclunitintvd |
|
147 |
|
expcncf |
|
148 |
44 147
|
syl |
|
149 |
112 121 148 124 71
|
cncfcompt2 |
|
150 |
149
|
resclunitintvd |
|
151 |
146 150
|
mulcncf |
|
152 |
19 20 111 128 142 151
|
ftc2 |
|
153 |
|
eqidd |
|
154 |
|
simpr |
|
155 |
154
|
oveq2d |
|
156 |
155 3
|
eqtrdi |
|
157 |
156
|
oveq1d |
|
158 |
|
0exp |
|
159 |
1 158
|
syl |
|
160 |
159
|
adantr |
|
161 |
157 160
|
eqtrd |
|
162 |
161
|
oveq2d |
|
163 |
78
|
mul01d |
|
164 |
163
|
adantr |
|
165 |
162 164
|
eqtrd |
|
166 |
|
1elunit |
|
167 |
166
|
a1i |
|
168 |
|
0cnd |
|
169 |
153 165 167 168
|
fvmptd |
|
170 |
|
simpr |
|
171 |
170
|
oveq2d |
|
172 |
|
1m0e1 |
|
173 |
171 172
|
eqtrdi |
|
174 |
173
|
oveq1d |
|
175 |
44
|
nn0zd |
|
176 |
|
1exp |
|
177 |
175 176
|
syl |
|
178 |
177
|
adantr |
|
179 |
174 178
|
eqtrd |
|
180 |
179
|
oveq2d |
|
181 |
78
|
adantr |
|
182 |
181
|
mulid1d |
|
183 |
180 182
|
eqtrd |
|
184 |
|
0elunit |
|
185 |
184
|
a1i |
|
186 |
153 183 185 78
|
fvmptd |
|
187 |
169 186
|
oveq12d |
|
188 |
152 187
|
eqtrd |
|
189 |
|
df-neg |
|
190 |
189
|
a1i |
|
191 |
61 76 77
|
divnegd |
|
192 |
191
|
oveq2d |
|
193 |
190 192
|
eqtr2d |
|
194 |
76 77
|
reccld |
|
195 |
194
|
negnegd |
|
196 |
193 195
|
eqtrd |
|
197 |
188 196
|
eqtrd |
|
198 |
109 197
|
eqtr3d |
|
199 |
37 198
|
eqtr3d |
|
200 |
22 199
|
eqtr3d |
|
201 |
|
bcn1 |
|
202 |
44 201
|
syl |
|
203 |
202
|
oveq2d |
|
204 |
76
|
mulid2d |
|
205 |
203 204
|
eqtrd |
|
206 |
205
|
oveq2d |
|
207 |
200 206
|
eqtr4d |
|
208 |
18 207
|
eqtrd |
|