Step |
Hyp |
Ref |
Expression |
1 |
|
intfracq.1 |
|
2 |
|
intfracq.2 |
|
3 |
|
zre |
|
4 |
3
|
adantr |
|
5 |
|
nnre |
|
6 |
5
|
adantl |
|
7 |
|
nnne0 |
|
8 |
7
|
adantl |
|
9 |
4 6 8
|
redivcld |
|
10 |
1 2
|
intfrac2 |
|
11 |
9 10
|
syl |
|
12 |
11
|
simp1d |
|
13 |
|
fraclt1 |
|
14 |
9 13
|
syl |
|
15 |
1
|
oveq2i |
|
16 |
2 15
|
eqtri |
|
17 |
16
|
a1i |
|
18 |
|
nncn |
|
19 |
18 7
|
dividd |
|
20 |
19
|
adantl |
|
21 |
14 17 20
|
3brtr4d |
|
22 |
|
reflcl |
|
23 |
9 22
|
syl |
|
24 |
1 23
|
eqeltrid |
|
25 |
9 24
|
resubcld |
|
26 |
2 25
|
eqeltrid |
|
27 |
|
nngt0 |
|
28 |
5 27
|
jca |
|
29 |
28
|
adantl |
|
30 |
|
ltmuldiv2 |
|
31 |
26 6 29 30
|
syl3anc |
|
32 |
21 31
|
mpbird |
|
33 |
2
|
oveq2i |
|
34 |
18
|
adantl |
|
35 |
9
|
recnd |
|
36 |
9
|
flcld |
|
37 |
1 36
|
eqeltrid |
|
38 |
37
|
zcnd |
|
39 |
34 35 38
|
subdid |
|
40 |
33 39
|
eqtrid |
|
41 |
|
zcn |
|
42 |
41
|
adantr |
|
43 |
42 34 8
|
divcan2d |
|
44 |
|
simpl |
|
45 |
43 44
|
eqeltrd |
|
46 |
|
nnz |
|
47 |
46
|
adantl |
|
48 |
47 37
|
zmulcld |
|
49 |
45 48
|
zsubcld |
|
50 |
40 49
|
eqeltrd |
|
51 |
|
zltlem1 |
|
52 |
50 47 51
|
syl2anc |
|
53 |
32 52
|
mpbid |
|
54 |
|
peano2rem |
|
55 |
5 54
|
syl |
|
56 |
55
|
adantl |
|
57 |
|
lemuldiv2 |
|
58 |
26 56 29 57
|
syl3anc |
|
59 |
53 58
|
mpbid |
|
60 |
11
|
simp3d |
|
61 |
12 59 60
|
3jca |
|