Step |
Hyp |
Ref |
Expression |
1 |
|
limsupvaluz.m |
|
2 |
|
limsupvaluz.z |
|
3 |
|
limsupvaluz.f |
|
4 |
|
eqid |
|
5 |
2
|
fvexi |
|
6 |
5
|
a1i |
|
7 |
3 6
|
fexd |
|
8 |
7
|
elexd |
|
9 |
|
uzssre |
|
10 |
2 9
|
eqsstri |
|
11 |
10
|
a1i |
|
12 |
2
|
uzsup |
|
13 |
1 12
|
syl |
|
14 |
4 8 11 13
|
limsupval2 |
|
15 |
11
|
mptima2 |
|
16 |
|
oveq1 |
|
17 |
16
|
imaeq2d |
|
18 |
17
|
ineq1d |
|
19 |
18
|
supeq1d |
|
20 |
19
|
cbvmptv |
|
21 |
20
|
a1i |
|
22 |
|
fimass |
|
23 |
3 22
|
syl |
|
24 |
|
df-ss |
|
25 |
24
|
biimpi |
|
26 |
23 25
|
syl |
|
27 |
26
|
adantr |
|
28 |
|
df-ima |
|
29 |
28
|
a1i |
|
30 |
3
|
freld |
|
31 |
|
resindm |
|
32 |
30 31
|
syl |
|
33 |
32
|
adantr |
|
34 |
|
incom |
|
35 |
2
|
ineq1i |
|
36 |
34 35
|
eqtri |
|
37 |
36
|
a1i |
|
38 |
3
|
fdmd |
|
39 |
38
|
ineq2d |
|
40 |
39
|
adantr |
|
41 |
2
|
eleq2i |
|
42 |
41
|
biimpi |
|
43 |
42
|
adantl |
|
44 |
43
|
uzinico2 |
|
45 |
37 40 44
|
3eqtr4d |
|
46 |
45
|
reseq2d |
|
47 |
33 46
|
eqtr3d |
|
48 |
47
|
rneqd |
|
49 |
27 29 48
|
3eqtrd |
|
50 |
49
|
supeq1d |
|
51 |
50
|
mpteq2dva |
|
52 |
21 51
|
eqtrd |
|
53 |
52
|
rneqd |
|
54 |
15 53
|
eqtrd |
|
55 |
54
|
infeq1d |
|
56 |
|
fveq2 |
|
57 |
56
|
reseq2d |
|
58 |
57
|
rneqd |
|
59 |
58
|
supeq1d |
|
60 |
59
|
cbvmptv |
|
61 |
60
|
rneqi |
|
62 |
61
|
infeq1i |
|
63 |
62
|
a1i |
|
64 |
14 55 63
|
3eqtrd |
|