Step |
Hyp |
Ref |
Expression |
1 |
|
knoppndvlem21.t |
|
2 |
|
knoppndvlem21.f |
|
3 |
|
knoppndvlem21.w |
|
4 |
|
knoppndvlem21.g |
|
5 |
|
knoppndvlem21.c |
|
6 |
|
knoppndvlem21.d |
|
7 |
|
knoppndvlem21.e |
|
8 |
|
knoppndvlem21.h |
|
9 |
|
knoppndvlem21.j |
|
10 |
|
knoppndvlem21.n |
|
11 |
|
knoppndvlem21.1 |
|
12 |
|
knoppndvlem21.2 |
|
13 |
|
knoppndvlem21.3 |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
14 15 9 8 10
|
knoppndvlem19 |
|
17 |
|
2re |
|
18 |
17
|
a1i |
|
19 |
10
|
nnred |
|
20 |
18 19
|
remulcld |
|
21 |
|
2pos |
|
22 |
21
|
a1i |
|
23 |
10
|
nngt0d |
|
24 |
18 19 22 23
|
mulgt0d |
|
25 |
24
|
gt0ne0d |
|
26 |
9
|
nn0zd |
|
27 |
26
|
znegcld |
|
28 |
20 25 27
|
reexpclzd |
|
29 |
28
|
rehalfcld |
|
30 |
29
|
adantr |
|
31 |
|
simpr |
|
32 |
31
|
zred |
|
33 |
30 32
|
remulcld |
|
34 |
33
|
adantrr |
|
35 |
|
peano2re |
|
36 |
32 35
|
syl |
|
37 |
30 36
|
jca |
|
38 |
|
remulcl |
|
39 |
37 38
|
syl |
|
40 |
39
|
adantrr |
|
41 |
|
simprr |
|
42 |
9
|
adantr |
|
43 |
10
|
adantr |
|
44 |
14 15 42 31 43
|
knoppndvlem16 |
|
45 |
12
|
adantr |
|
46 |
44 45
|
eqbrtrd |
|
47 |
20 27 24
|
3jca |
|
48 |
|
expgt0 |
|
49 |
47 48
|
syl |
|
50 |
28 18 49 22
|
divgt0d |
|
51 |
50
|
adantr |
|
52 |
44
|
eqcomd |
|
53 |
51 52
|
breqtrd |
|
54 |
33 39
|
posdifd |
|
55 |
53 54
|
mpbird |
|
56 |
33 55
|
ltned |
|
57 |
46 56
|
jca |
|
58 |
57
|
adantrr |
|
59 |
7
|
rpred |
|
60 |
59
|
adantr |
|
61 |
5
|
knoppndvlem3 |
|
62 |
61
|
simpld |
|
63 |
62
|
recnd |
|
64 |
63
|
abscld |
|
65 |
20 64
|
remulcld |
|
66 |
65 9
|
reexpcld |
|
67 |
4
|
a1i |
|
68 |
5 10 11
|
knoppndvlem20 |
|
69 |
68
|
rpred |
|
70 |
67 69
|
eqeltrd |
|
71 |
66 70
|
remulcld |
|
72 |
71
|
adantr |
|
73 |
62
|
adantr |
|
74 |
61
|
simprd |
|
75 |
74
|
adantr |
|
76 |
1 2 3 39 43 73 75
|
knoppcld |
|
77 |
1 2 3 33 43 73 75
|
knoppcld |
|
78 |
76 77
|
subcld |
|
79 |
78
|
abscld |
|
80 |
44 30
|
eqeltrd |
|
81 |
53
|
gt0ne0d |
|
82 |
79 80 81
|
redivcld |
|
83 |
13
|
adantr |
|
84 |
4
|
oveq2i |
|
85 |
84
|
a1i |
|
86 |
5
|
adantr |
|
87 |
11
|
adantr |
|
88 |
1 2 3 14 15 86 42 31 43 87
|
knoppndvlem17 |
|
89 |
85 88
|
eqbrtrd |
|
90 |
60 72 82 83 89
|
letrd |
|
91 |
90
|
adantrr |
|
92 |
41 58 91
|
3jca |
|
93 |
34 40 92
|
3jca |
|
94 |
|
breq1 |
|
95 |
94
|
anbi1d |
|
96 |
|
oveq2 |
|
97 |
96
|
breq1d |
|
98 |
|
neeq1 |
|
99 |
97 98
|
anbi12d |
|
100 |
|
fveq2 |
|
101 |
100
|
oveq2d |
|
102 |
101
|
fveq2d |
|
103 |
102 96
|
oveq12d |
|
104 |
103
|
breq2d |
|
105 |
95 99 104
|
3anbi123d |
|
106 |
|
breq2 |
|
107 |
106
|
anbi2d |
|
108 |
|
oveq1 |
|
109 |
108
|
breq1d |
|
110 |
|
neeq2 |
|
111 |
109 110
|
anbi12d |
|
112 |
|
fveq2 |
|
113 |
112
|
fvoveq1d |
|
114 |
113 108
|
oveq12d |
|
115 |
114
|
breq2d |
|
116 |
107 111 115
|
3anbi123d |
|
117 |
105 116
|
rspc2ev |
|
118 |
93 117
|
syl |
|
119 |
16 118
|
rexlimddv |
|