Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem.1 |
|
2 |
|
lcmineqlem.2 |
|
3 |
|
7re |
|
4 |
3
|
a1i |
|
5 |
1
|
nnred |
|
6 |
4 5
|
leloed |
|
7 |
1
|
nnzd |
|
8 |
|
7nn |
|
9 |
8
|
nnzi |
|
10 |
|
zltp1le |
|
11 |
9 10
|
mpan |
|
12 |
7 11
|
syl |
|
13 |
|
7p1e8 |
|
14 |
13
|
breq1i |
|
15 |
12 14
|
syl6bb |
|
16 |
|
8re |
|
17 |
16
|
a1i |
|
18 |
17 5
|
leloed |
|
19 |
1
|
adantr |
|
20 |
|
8p1e9 |
|
21 |
|
8nn |
|
22 |
21
|
nnzi |
|
23 |
|
zltp1le |
|
24 |
22 23
|
mpan |
|
25 |
7 24
|
syl |
|
26 |
25
|
biimpd |
|
27 |
26
|
imp |
|
28 |
20 27
|
eqbrtrrid |
|
29 |
19 28
|
lcmineqlem23 |
|
30 |
29
|
ex |
|
31 |
|
2nn0 |
|
32 |
|
8nn0 |
|
33 |
|
5nn0 |
|
34 |
|
4nn0 |
|
35 |
|
6nn0 |
|
36 |
|
0nn0 |
|
37 |
|
2lt8 |
|
38 |
|
5lt10 |
|
39 |
|
6lt10 |
|
40 |
31 32 33 34 35 36 37 38 39
|
3decltc |
|
41 |
|
5nn |
|
42 |
31 41
|
decnncl |
|
43 |
42
|
nnnn0i |
|
44 |
|
6nn |
|
45 |
43 44
|
decnncl |
|
46 |
45
|
nnrei |
|
47 |
|
4nn |
|
48 |
32 47
|
decnncl |
|
49 |
48
|
decnncl2 |
|
50 |
49
|
nnrei |
|
51 |
46 50
|
ltlei |
|
52 |
40 51
|
ax-mp |
|
53 |
|
2exp8 |
|
54 |
|
oveq2 |
|
55 |
53 54
|
syl5eqr |
|
56 |
|
lcm8un |
|
57 |
|
oveq2 |
|
58 |
57
|
fveq2d |
|
59 |
56 58
|
syl5eqr |
|
60 |
55 59
|
breq12d |
|
61 |
52 60
|
mpbii |
|
62 |
61
|
adantl |
|
63 |
62
|
ex |
|
64 |
30 63
|
jaod |
|
65 |
18 64
|
sylbid |
|
66 |
15 65
|
sylbid |
|
67 |
|
1nn0 |
|
68 |
|
1lt4 |
|
69 |
|
2lt10 |
|
70 |
|
8lt10 |
|
71 |
67 34 31 31 32 36 68 69 70
|
3decltc |
|
72 |
|
2nn |
|
73 |
67 72
|
decnncl |
|
74 |
73
|
nnnn0i |
|
75 |
74 21
|
decnncl |
|
76 |
75
|
nnrei |
|
77 |
34 72
|
decnncl |
|
78 |
77
|
decnncl2 |
|
79 |
78
|
nnrei |
|
80 |
76 79
|
ltlei |
|
81 |
71 80
|
ax-mp |
|
82 |
|
2exp7 |
|
83 |
|
oveq2 |
|
84 |
82 83
|
syl5eqr |
|
85 |
|
lcm7un |
|
86 |
|
oveq2 |
|
87 |
86
|
fveq2d |
|
88 |
85 87
|
syl5eqr |
|
89 |
84 88
|
breq12d |
|
90 |
81 89
|
mpbii |
|
91 |
90
|
a1i |
|
92 |
66 91
|
jaod |
|
93 |
6 92
|
sylbid |
|
94 |
2 93
|
mpd |
|