Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem13.1 |
|
2 |
|
lcmineqlem13.2 |
|
3 |
|
lcmineqlem13.3 |
|
4 |
|
lcmineqlem13.4 |
|
5 |
2
|
nnzd |
|
6 |
|
nnge1 |
|
7 |
2 6
|
syl |
|
8 |
5 7 4
|
3jca |
|
9 |
|
oveq1 |
|
10 |
9
|
oveq2d |
|
11 |
|
oveq2 |
|
12 |
11
|
oveq2d |
|
13 |
10 12
|
oveq12d |
|
14 |
13
|
adantr |
|
15 |
14
|
itgeq2dv |
|
16 |
|
id |
|
17 |
|
oveq2 |
|
18 |
16 17
|
oveq12d |
|
19 |
18
|
oveq2d |
|
20 |
15 19
|
eqeq12d |
|
21 |
|
oveq1 |
|
22 |
21
|
oveq2d |
|
23 |
|
oveq2 |
|
24 |
23
|
oveq2d |
|
25 |
22 24
|
oveq12d |
|
26 |
25
|
adantr |
|
27 |
26
|
itgeq2dv |
|
28 |
|
id |
|
29 |
|
oveq2 |
|
30 |
28 29
|
oveq12d |
|
31 |
30
|
oveq2d |
|
32 |
27 31
|
eqeq12d |
|
33 |
|
oveq1 |
|
34 |
33
|
oveq2d |
|
35 |
|
oveq2 |
|
36 |
35
|
oveq2d |
|
37 |
34 36
|
oveq12d |
|
38 |
37
|
adantr |
|
39 |
38
|
itgeq2dv |
|
40 |
|
id |
|
41 |
|
oveq2 |
|
42 |
40 41
|
oveq12d |
|
43 |
42
|
oveq2d |
|
44 |
39 43
|
eqeq12d |
|
45 |
|
oveq1 |
|
46 |
45
|
oveq2d |
|
47 |
|
oveq2 |
|
48 |
47
|
oveq2d |
|
49 |
46 48
|
oveq12d |
|
50 |
49
|
adantr |
|
51 |
50
|
itgeq2dv |
|
52 |
|
id |
|
53 |
|
oveq2 |
|
54 |
52 53
|
oveq12d |
|
55 |
54
|
oveq2d |
|
56 |
51 55
|
eqeq12d |
|
57 |
3
|
lcmineqlem12 |
|
58 |
|
elnnz1 |
|
59 |
58
|
biimpri |
|
60 |
59
|
3adant3 |
|
61 |
60
|
adantl |
|
62 |
3
|
adantr |
|
63 |
|
simpr3 |
|
64 |
61 62 63
|
lcmineqlem10 |
|
65 |
64
|
3adant3 |
|
66 |
|
oveq2 |
|
67 |
66
|
3ad2ant3 |
|
68 |
65 67
|
eqtrd |
|
69 |
61 62 63
|
lcmineqlem11 |
|
70 |
69
|
3adant3 |
|
71 |
68 70
|
eqtr4d |
|
72 |
|
1zzd |
|
73 |
3
|
nnzd |
|
74 |
3
|
nnge1d |
|
75 |
20 32 44 56 57 71 72 73 74
|
fzindd |
|
76 |
8 75
|
mpdan |
|
77 |
1 76
|
syl5eq |
|