Step |
Hyp |
Ref |
Expression |
1 |
|
lgsdilem2.1 |
|
2 |
|
lgsdilem2.2 |
|
3 |
|
lgsdilem2.3 |
|
4 |
|
lgsdilem2.4 |
|
5 |
|
lgsdilem2.5 |
|
6 |
|
lgsdilem2.6 |
|
7 |
|
mulid1 |
|
8 |
7
|
adantl |
|
9 |
|
nnabscl |
|
10 |
2 4 9
|
syl2anc |
|
11 |
|
nnuz |
|
12 |
10 11
|
eleqtrdi |
|
13 |
10
|
nnzd |
|
14 |
2 3
|
zmulcld |
|
15 |
2
|
zcnd |
|
16 |
3
|
zcnd |
|
17 |
15 16 4 5
|
mulne0d |
|
18 |
|
nnabscl |
|
19 |
14 17 18
|
syl2anc |
|
20 |
19
|
nnzd |
|
21 |
15
|
abscld |
|
22 |
16
|
abscld |
|
23 |
15
|
absge0d |
|
24 |
|
nnabscl |
|
25 |
3 5 24
|
syl2anc |
|
26 |
25
|
nnge1d |
|
27 |
21 22 23 26
|
lemulge11d |
|
28 |
15 16
|
absmuld |
|
29 |
27 28
|
breqtrrd |
|
30 |
|
eluz2 |
|
31 |
13 20 29 30
|
syl3anbrc |
|
32 |
6
|
lgsfcl3 |
|
33 |
1 2 4 32
|
syl3anc |
|
34 |
|
elfznn |
|
35 |
|
ffvelrn |
|
36 |
33 34 35
|
syl2an |
|
37 |
36
|
zcnd |
|
38 |
|
mulcl |
|
39 |
38
|
adantl |
|
40 |
12 37 39
|
seqcl |
|
41 |
10
|
peano2nnd |
|
42 |
|
elfzuz |
|
43 |
|
eluznn |
|
44 |
41 42 43
|
syl2an |
|
45 |
|
eleq1w |
|
46 |
|
oveq2 |
|
47 |
|
oveq1 |
|
48 |
46 47
|
oveq12d |
|
49 |
45 48
|
ifbieq1d |
|
50 |
|
ovex |
|
51 |
|
1ex |
|
52 |
50 51
|
ifex |
|
53 |
49 6 52
|
fvmpt |
|
54 |
44 53
|
syl |
|
55 |
|
simpr |
|
56 |
2
|
ad2antrr |
|
57 |
|
zq |
|
58 |
56 57
|
syl |
|
59 |
|
pcabs |
|
60 |
55 58 59
|
syl2anc |
|
61 |
|
elfzle1 |
|
62 |
61
|
adantl |
|
63 |
|
elfzelz |
|
64 |
|
zltp1le |
|
65 |
13 63 64
|
syl2an |
|
66 |
62 65
|
mpbird |
|
67 |
21
|
adantr |
|
68 |
63
|
adantl |
|
69 |
68
|
zred |
|
70 |
67 69
|
ltnled |
|
71 |
66 70
|
mpbid |
|
72 |
71
|
adantr |
|
73 |
|
prmz |
|
74 |
73
|
adantl |
|
75 |
4
|
ad2antrr |
|
76 |
56 75 9
|
syl2anc |
|
77 |
|
dvdsle |
|
78 |
74 76 77
|
syl2anc |
|
79 |
72 78
|
mtod |
|
80 |
|
pceq0 |
|
81 |
55 76 80
|
syl2anc |
|
82 |
79 81
|
mpbird |
|
83 |
60 82
|
eqtr3d |
|
84 |
83
|
oveq2d |
|
85 |
1
|
ad2antrr |
|
86 |
|
lgscl |
|
87 |
85 74 86
|
syl2anc |
|
88 |
87
|
zcnd |
|
89 |
88
|
exp0d |
|
90 |
84 89
|
eqtrd |
|
91 |
90
|
ifeq1da |
|
92 |
|
ifid |
|
93 |
91 92
|
eqtrdi |
|
94 |
54 93
|
eqtrd |
|
95 |
8 12 31 40 94
|
seqid2 |
|