Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem18.1 |
|
2 |
|
0zd |
|
3 |
|
2z |
|
4 |
3
|
a1i |
|
5 |
1
|
nnzd |
|
6 |
4 5
|
zmulcld |
|
7 |
6
|
peano2zd |
|
8 |
5
|
peano2zd |
|
9 |
2 7 8
|
3jca |
|
10 |
1
|
nnred |
|
11 |
|
1red |
|
12 |
1
|
nnnn0d |
|
13 |
12
|
nn0ge0d |
|
14 |
|
0le1 |
|
15 |
14
|
a1i |
|
16 |
10 11 13 15
|
addge0d |
|
17 |
10 11
|
readdcld |
|
18 |
17 10
|
addge01d |
|
19 |
13 18
|
mpbid |
|
20 |
10
|
recnd |
|
21 |
|
1cnd |
|
22 |
20 21 20
|
add32d |
|
23 |
20
|
2timesd |
|
24 |
23
|
oveq1d |
|
25 |
24
|
eqcomd |
|
26 |
22 25
|
eqtrd |
|
27 |
19 26
|
breqtrd |
|
28 |
16 27
|
jca |
|
29 |
9 28
|
jca |
|
30 |
|
elfz2 |
|
31 |
29 30
|
sylibr |
|
32 |
|
bcval2 |
|
33 |
31 32
|
syl |
|
34 |
6
|
zcnd |
|
35 |
34 21 20 21
|
addsub4d |
|
36 |
23
|
oveq1d |
|
37 |
20 20
|
pncand |
|
38 |
36 37
|
eqtrd |
|
39 |
|
1m1e0 |
|
40 |
39
|
a1i |
|
41 |
38 40
|
oveq12d |
|
42 |
20
|
addid1d |
|
43 |
41 42
|
eqtrd |
|
44 |
35 43
|
eqtrd |
|
45 |
44
|
fveq2d |
|
46 |
45
|
oveq1d |
|
47 |
46
|
oveq2d |
|
48 |
33 47
|
eqtrd |
|
49 |
|
faccl |
|
50 |
12 49
|
syl |
|
51 |
50
|
nncnd |
|
52 |
|
1nn0 |
|
53 |
52
|
a1i |
|
54 |
12 53
|
nn0addcld |
|
55 |
|
faccl |
|
56 |
54 55
|
syl |
|
57 |
56
|
nncnd |
|
58 |
51 57
|
mulcomd |
|
59 |
|
facp1 |
|
60 |
12 59
|
syl |
|
61 |
20 21
|
addcld |
|
62 |
51 61
|
mulcomd |
|
63 |
60 62
|
eqtrd |
|
64 |
63
|
oveq1d |
|
65 |
61 51 51
|
mulassd |
|
66 |
64 65
|
eqtrd |
|
67 |
58 66
|
eqtrd |
|
68 |
67
|
oveq2d |
|
69 |
48 68
|
eqtrd |
|
70 |
|
2nn0 |
|
71 |
70
|
a1i |
|
72 |
71 12
|
nn0mulcld |
|
73 |
|
facp1 |
|
74 |
72 73
|
syl |
|
75 |
|
faccl |
|
76 |
72 75
|
syl |
|
77 |
76
|
nncnd |
|
78 |
34 21
|
addcld |
|
79 |
77 78
|
mulcomd |
|
80 |
74 79
|
eqtrd |
|
81 |
80
|
oveq1d |
|
82 |
69 81
|
eqtrd |
|
83 |
82
|
oveq2d |
|
84 |
78 77
|
mulcld |
|
85 |
51 51
|
mulcld |
|
86 |
61 85
|
mulcld |
|
87 |
1
|
peano2nnd |
|
88 |
87
|
nnne0d |
|
89 |
50
|
nnne0d |
|
90 |
51 51 89 89
|
mulne0d |
|
91 |
61 85 88 90
|
mulne0d |
|
92 |
61 84 86 91
|
divassd |
|
93 |
92
|
eqcomd |
|
94 |
83 93
|
eqtrd |
|
95 |
61 61 84 85 88 90
|
divmuldivd |
|
96 |
95
|
eqcomd |
|
97 |
94 96
|
eqtrd |
|
98 |
61 88
|
dividd |
|
99 |
98
|
oveq1d |
|
100 |
84 85 90
|
divcld |
|
101 |
100
|
mulid2d |
|
102 |
99 101
|
eqtrd |
|
103 |
97 102
|
eqtrd |
|
104 |
78 77 85 90
|
divassd |
|
105 |
103 104
|
eqtrd |
|
106 |
2 6 5
|
3jca |
|
107 |
10 10
|
addge01d |
|
108 |
23
|
breq2d |
|
109 |
107 108
|
bitr4d |
|
110 |
13 109
|
mpbid |
|
111 |
13 110
|
jca |
|
112 |
106 111
|
jca |
|
113 |
|
elfz2 |
|
114 |
112 113
|
sylibr |
|
115 |
|
bcval2 |
|
116 |
114 115
|
syl |
|
117 |
38
|
fveq2d |
|
118 |
117
|
oveq1d |
|
119 |
118
|
oveq2d |
|
120 |
116 119
|
eqtrd |
|
121 |
120
|
oveq2d |
|
122 |
121
|
eqcomd |
|
123 |
105 122
|
eqtrd |
|