Step |
Hyp |
Ref |
Expression |
1 |
|
knoppcnlem4.t |
|
2 |
|
knoppcnlem4.f |
|
3 |
|
knoppcnlem4.n |
|
4 |
|
knoppcnlem4.1 |
|
5 |
|
knoppcnlem4.2 |
|
6 |
|
knoppcnlem4.3 |
|
7 |
2 5 6
|
knoppcnlem1 |
|
8 |
7
|
fveq2d |
|
9 |
4
|
recnd |
|
10 |
9 6
|
expcld |
|
11 |
|
2re |
|
12 |
11
|
a1i |
|
13 |
|
nnre |
|
14 |
3 13
|
syl |
|
15 |
12 14
|
remulcld |
|
16 |
15 6
|
reexpcld |
|
17 |
16 5
|
remulcld |
|
18 |
1 17
|
dnicld2 |
|
19 |
18
|
recnd |
|
20 |
10 19
|
absmuld |
|
21 |
9 6
|
absexpd |
|
22 |
21
|
oveq1d |
|
23 |
20 22
|
eqtrd |
|
24 |
19
|
abscld |
|
25 |
|
1red |
|
26 |
9
|
abscld |
|
27 |
26 6
|
reexpcld |
|
28 |
9
|
absge0d |
|
29 |
26 6 28
|
expge0d |
|
30 |
1
|
dnival |
|
31 |
17 30
|
syl |
|
32 |
31
|
fveq2d |
|
33 |
|
halfre |
|
34 |
33
|
a1i |
|
35 |
17 34
|
readdcld |
|
36 |
|
reflcl |
|
37 |
35 36
|
syl |
|
38 |
37 17
|
resubcld |
|
39 |
38
|
recnd |
|
40 |
|
absidm |
|
41 |
39 40
|
syl |
|
42 |
32 41
|
eqtrd |
|
43 |
31 18
|
eqeltrrd |
|
44 |
|
rddif |
|
45 |
17 44
|
syl |
|
46 |
|
halflt1 |
|
47 |
|
1re |
|
48 |
33 47
|
ltlei |
|
49 |
46 48
|
ax-mp |
|
50 |
49
|
a1i |
|
51 |
43 34 25 45 50
|
letrd |
|
52 |
42 51
|
eqbrtrd |
|
53 |
24 25 27 29 52
|
lemul2ad |
|
54 |
|
ax-1rid |
|
55 |
27 54
|
syl |
|
56 |
53 55
|
breqtrd |
|
57 |
23 56
|
eqbrtrd |
|
58 |
|
eqidd |
|
59 |
|
oveq2 |
|
60 |
59
|
adantl |
|
61 |
58 60 6 27
|
fvmptd |
|
62 |
61
|
eqcomd |
|
63 |
57 62
|
breqtrd |
|
64 |
8 63
|
eqbrtrd |
|