Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem6.1 |
|
2 |
|
lcmineqlem6.2 |
|
3 |
|
lcmineqlem6.3 |
|
4 |
|
lcmineqlem6.4 |
|
5 |
1 2 3 4
|
lcmineqlem3 |
|
6 |
5
|
oveq2d |
|
7 |
|
fzfid |
|
8 |
|
fz1ssnn |
|
9 |
|
fzfi |
|
10 |
8 9
|
pm3.2i |
|
11 |
|
lcmfnncl |
|
12 |
10 11
|
ax-mp |
|
13 |
12
|
nncni |
|
14 |
13
|
a1i |
|
15 |
|
elfzelz |
|
16 |
|
m1expcl |
|
17 |
15 16
|
syl |
|
18 |
17
|
zcnd |
|
19 |
18
|
adantl |
|
20 |
|
bccl2 |
|
21 |
20
|
nncnd |
|
22 |
21
|
adantl |
|
23 |
19 22
|
mulcld |
|
24 |
3
|
nncnd |
|
25 |
24
|
adantr |
|
26 |
15
|
zcnd |
|
27 |
26
|
adantl |
|
28 |
25 27
|
addcld |
|
29 |
|
elfznn0 |
|
30 |
|
nnnn0addcl |
|
31 |
29 30
|
sylan2 |
|
32 |
3 31
|
sylan |
|
33 |
32
|
nnne0d |
|
34 |
28 33
|
reccld |
|
35 |
23 34
|
mulcld |
|
36 |
7 14 35
|
fsummulc2 |
|
37 |
6 36
|
eqtrd |
|
38 |
13
|
a1i |
|
39 |
38 23 28 33
|
lcmineqlem5 |
|
40 |
39
|
sumeq2dv |
|
41 |
37 40
|
eqtrd |
|
42 |
17
|
adantl |
|
43 |
20
|
nnzd |
|
44 |
43
|
adantl |
|
45 |
42 44
|
zmulcld |
|
46 |
2
|
adantr |
|
47 |
3
|
adantr |
|
48 |
4
|
adantr |
|
49 |
|
simpr |
|
50 |
46 47 48 49
|
lcmineqlem4 |
|
51 |
45 50
|
zmulcld |
|
52 |
7 51
|
fsumzcl |
|
53 |
41 52
|
eqeltrd |
|