Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem22.1 |
|
2 |
|
lcmineqlem22.2 |
|
3 |
|
2re |
|
4 |
3
|
a1i |
|
5 |
|
2nn0 |
|
6 |
5
|
a1i |
|
7 |
1
|
nnnn0d |
|
8 |
6 7
|
nn0mulcld |
|
9 |
|
1nn0 |
|
10 |
9
|
a1i |
|
11 |
8 10
|
nn0addcld |
|
12 |
4 11
|
reexpcld |
|
13 |
8 6
|
nn0addcld |
|
14 |
4 13
|
reexpcld |
|
15 |
|
fz1ssnn |
|
16 |
|
fzfi |
|
17 |
|
lcmfnncl |
|
18 |
15 16 17
|
mp2an |
|
19 |
18
|
a1i |
|
20 |
19
|
nnred |
|
21 |
|
1red |
|
22 |
1
|
nnred |
|
23 |
4 22
|
remulcld |
|
24 |
|
1lt2 |
|
25 |
24
|
a1i |
|
26 |
21 4 25
|
ltled |
|
27 |
21 4 23 26
|
leadd2dd |
|
28 |
|
2z |
|
29 |
28
|
a1i |
|
30 |
1
|
nnzd |
|
31 |
29 30
|
zmulcld |
|
32 |
31
|
peano2zd |
|
33 |
31 29
|
zaddcld |
|
34 |
4 32 33 25
|
leexp2d |
|
35 |
27 34
|
mpbid |
|
36 |
1 2
|
lcmineqlem21 |
|
37 |
12 14 20 35 36
|
letrd |
|
38 |
|
fz1ssnn |
|
39 |
|
fzfi |
|
40 |
|
lcmfnncl |
|
41 |
38 39 40
|
mp2an |
|
42 |
41
|
a1i |
|
43 |
42
|
nnred |
|
44 |
19
|
nnzd |
|
45 |
44 33
|
jca |
|
46 |
|
dvdslcm |
|
47 |
45 46
|
syl |
|
48 |
47
|
simpld |
|
49 |
|
2nn |
|
50 |
49
|
a1i |
|
51 |
50 1
|
nnmulcld |
|
52 |
51 50
|
nnaddcld |
|
53 |
52
|
lcmfunnnd |
|
54 |
23
|
recnd |
|
55 |
4
|
recnd |
|
56 |
|
1cnd |
|
57 |
54 55 56
|
addsubassd |
|
58 |
|
2m1e1 |
|
59 |
58
|
oveq2i |
|
60 |
57 59
|
eqtrdi |
|
61 |
60
|
oveq2d |
|
62 |
61
|
fveq2d |
|
63 |
62
|
oveq1d |
|
64 |
53 63
|
eqtrd |
|
65 |
48 64
|
breqtrrd |
|
66 |
44 42
|
jca |
|
67 |
|
dvdsle |
|
68 |
66 67
|
syl |
|
69 |
65 68
|
mpd |
|
70 |
14 20 43 36 69
|
letrd |
|
71 |
37 70
|
jca |
|