Step |
Hyp |
Ref |
Expression |
1 |
|
sge0p1.1 |
|
2 |
|
sge0p1.2 |
|
3 |
|
sge0p1.3 |
|
4 |
|
fzsuc |
|
5 |
1 4
|
syl |
|
6 |
5
|
mpteq1d |
|
7 |
6
|
fveq2d |
|
8 |
|
nfv |
|
9 |
|
ovex |
|
10 |
9
|
a1i |
|
11 |
|
snex |
|
12 |
11
|
a1i |
|
13 |
|
fzp1disj |
|
14 |
13
|
a1i |
|
15 |
|
0xr |
|
16 |
15
|
a1i |
|
17 |
|
pnfxr |
|
18 |
17
|
a1i |
|
19 |
|
iccssxr |
|
20 |
|
simpl |
|
21 |
|
fzelp1 |
|
22 |
21
|
adantl |
|
23 |
20 22 2
|
syl2anc |
|
24 |
19 23
|
sseldi |
|
25 |
|
iccgelb |
|
26 |
16 18 23 25
|
syl3anc |
|
27 |
|
iccleub |
|
28 |
16 18 23 27
|
syl3anc |
|
29 |
16 18 24 26 28
|
eliccxrd |
|
30 |
|
simpl |
|
31 |
|
elsni |
|
32 |
31
|
adantl |
|
33 |
|
simpr |
|
34 |
|
peano2uz |
|
35 |
|
eluzfz2 |
|
36 |
1 34 35
|
3syl |
|
37 |
36
|
adantr |
|
38 |
33 37
|
eqeltrd |
|
39 |
30 32 38
|
syl2anc |
|
40 |
30 39 2
|
syl2anc |
|
41 |
8 10 12 14 29 40
|
sge0splitmpt |
|
42 |
|
ovex |
|
43 |
42
|
a1i |
|
44 |
|
id |
|
45 |
|
eleq1 |
|
46 |
45
|
anbi2d |
|
47 |
3
|
eleq1d |
|
48 |
46 47
|
imbi12d |
|
49 |
48 2
|
vtoclg |
|
50 |
42 49
|
ax-mp |
|
51 |
44 36 50
|
syl2anc |
|
52 |
43 51 3
|
sge0snmpt |
|
53 |
52
|
oveq2d |
|
54 |
7 41 53
|
3eqtrd |
|