Step |
Hyp |
Ref |
Expression |
1 |
|
quorem.1 |
|
2 |
|
quorem.2 |
|
3 |
|
fldivnn0 |
|
4 |
1 3
|
eqeltrid |
|
5 |
|
nnnn0 |
|
6 |
5
|
adantl |
|
7 |
6 4
|
nn0mulcld |
|
8 |
|
simpl |
|
9 |
4
|
nn0cnd |
|
10 |
|
nncn |
|
11 |
10
|
adantl |
|
12 |
|
nnne0 |
|
13 |
12
|
adantl |
|
14 |
9 11 13
|
divcan3d |
|
15 |
|
nn0nndivcl |
|
16 |
|
flle |
|
17 |
15 16
|
syl |
|
18 |
1 17
|
eqbrtrid |
|
19 |
14 18
|
eqbrtrd |
|
20 |
7
|
nn0red |
|
21 |
|
nn0re |
|
22 |
21
|
adantr |
|
23 |
|
nnre |
|
24 |
23
|
adantl |
|
25 |
|
nngt0 |
|
26 |
25
|
adantl |
|
27 |
|
lediv1 |
|
28 |
20 22 24 26 27
|
syl112anc |
|
29 |
19 28
|
mpbird |
|
30 |
|
nn0sub2 |
|
31 |
7 8 29 30
|
syl3anc |
|
32 |
2 31
|
eqeltrid |
|
33 |
1
|
oveq2i |
|
34 |
|
fraclt1 |
|
35 |
15 34
|
syl |
|
36 |
33 35
|
eqbrtrid |
|
37 |
2
|
oveq1i |
|
38 |
|
nn0cn |
|
39 |
38
|
adantr |
|
40 |
7
|
nn0cnd |
|
41 |
10 12
|
jca |
|
42 |
41
|
adantl |
|
43 |
|
divsubdir |
|
44 |
39 40 42 43
|
syl3anc |
|
45 |
14
|
oveq2d |
|
46 |
44 45
|
eqtrd |
|
47 |
37 46
|
eqtrid |
|
48 |
10 12
|
dividd |
|
49 |
48
|
adantl |
|
50 |
36 47 49
|
3brtr4d |
|
51 |
32
|
nn0red |
|
52 |
|
ltdiv1 |
|
53 |
51 24 24 26 52
|
syl112anc |
|
54 |
50 53
|
mpbird |
|
55 |
2
|
oveq2i |
|
56 |
40 39
|
pncan3d |
|
57 |
55 56
|
eqtr2id |
|
58 |
54 57
|
jca |
|
59 |
4 32 58
|
jca31 |
|