Step |
Hyp |
Ref |
Expression |
1 |
|
knoppndvlem14.t |
|
2 |
|
knoppndvlem14.f |
|
3 |
|
knoppndvlem14.a |
|
4 |
|
knoppndvlem14.b |
|
5 |
|
knoppndvlem14.c |
|
6 |
|
knoppndvlem14.j |
|
7 |
|
knoppndvlem14.m |
|
8 |
|
knoppndvlem14.n |
|
9 |
|
knoppndvlem14.1 |
|
10 |
4
|
a1i |
|
11 |
6
|
nn0zd |
|
12 |
7
|
peano2zd |
|
13 |
8 11 12
|
knoppndvlem1 |
|
14 |
10 13
|
eqeltrd |
|
15 |
5
|
knoppndvlem3 |
|
16 |
15
|
simpld |
|
17 |
1 2 14 16 8
|
knoppndvlem5 |
|
18 |
3
|
a1i |
|
19 |
8 11 7
|
knoppndvlem1 |
|
20 |
18 19
|
eqeltrd |
|
21 |
1 2 20 16 8
|
knoppndvlem5 |
|
22 |
17 21
|
resubcld |
|
23 |
22
|
recnd |
|
24 |
23
|
abscld |
|
25 |
14 20
|
resubcld |
|
26 |
25
|
recnd |
|
27 |
26
|
abscld |
|
28 |
|
fzfid |
|
29 |
|
2re |
|
30 |
29
|
a1i |
|
31 |
|
nnre |
|
32 |
8 31
|
syl |
|
33 |
30 32
|
remulcld |
|
34 |
16
|
recnd |
|
35 |
34
|
abscld |
|
36 |
33 35
|
remulcld |
|
37 |
36
|
adantr |
|
38 |
|
elfznn0 |
|
39 |
38
|
adantl |
|
40 |
37 39
|
reexpcld |
|
41 |
28 40
|
fsumrecl |
|
42 |
27 41
|
remulcld |
|
43 |
35 6
|
reexpcld |
|
44 |
|
2ne0 |
|
45 |
44
|
a1i |
|
46 |
43 30 45
|
redivcld |
|
47 |
|
1red |
|
48 |
36 47
|
resubcld |
|
49 |
|
0red |
|
50 |
|
0lt1 |
|
51 |
50
|
a1i |
|
52 |
5 8 9
|
knoppndvlem12 |
|
53 |
52
|
simprd |
|
54 |
49 47 48 51 53
|
lttrd |
|
55 |
49 54
|
jca |
|
56 |
|
ltne |
|
57 |
55 56
|
syl |
|
58 |
47 48 57
|
redivcld |
|
59 |
46 58
|
remulcld |
|
60 |
1 2 20 14 5 6 8
|
knoppndvlem11 |
|
61 |
10 18
|
oveq12d |
|
62 |
30
|
recnd |
|
63 |
32
|
recnd |
|
64 |
|
nnge1 |
|
65 |
8 64
|
syl |
|
66 |
49 47 32 51 65
|
ltletrd |
|
67 |
49 66
|
jca |
|
68 |
|
ltne |
|
69 |
67 68
|
syl |
|
70 |
62 63 45 69
|
mulne0d |
|
71 |
11
|
znegcld |
|
72 |
33 70 71
|
reexpclzd |
|
73 |
72 30 45
|
redivcld |
|
74 |
73
|
recnd |
|
75 |
12
|
zcnd |
|
76 |
7
|
zcnd |
|
77 |
74 75 76
|
subdid |
|
78 |
77
|
eqcomd |
|
79 |
|
1cnd |
|
80 |
76 79
|
pncan2d |
|
81 |
80
|
oveq2d |
|
82 |
74
|
mulid1d |
|
83 |
78 81 82
|
3eqtrd |
|
84 |
61 83
|
eqtrd |
|
85 |
84
|
fveq2d |
|
86 |
72
|
recnd |
|
87 |
86 62 45
|
absdivd |
|
88 |
62 63
|
mulcld |
|
89 |
88 70 71
|
3jca |
|
90 |
|
absexpz |
|
91 |
89 90
|
syl |
|
92 |
62 63
|
absmuld |
|
93 |
|
0le2 |
|
94 |
29 93
|
pm3.2i |
|
95 |
|
absid |
|
96 |
94 95
|
ax-mp |
|
97 |
96
|
a1i |
|
98 |
49 32 66
|
ltled |
|
99 |
32 98
|
absidd |
|
100 |
97 99
|
oveq12d |
|
101 |
92 100
|
eqtrd |
|
102 |
101
|
oveq1d |
|
103 |
91 102
|
eqtrd |
|
104 |
103 97
|
oveq12d |
|
105 |
87 104
|
eqtrd |
|
106 |
85 105
|
eqtrd |
|
107 |
36
|
recnd |
|
108 |
52
|
simpld |
|
109 |
107 108 6
|
geoser |
|
110 |
107 6
|
expcld |
|
111 |
108
|
necomd |
|
112 |
79 110 79 107 111
|
div2subd |
|
113 |
109 112
|
eqtrd |
|
114 |
106 113
|
oveq12d |
|
115 |
113 41
|
eqeltrrd |
|
116 |
36 6
|
reexpcld |
|
117 |
116 48 57
|
redivcld |
|
118 |
|
2rp |
|
119 |
118
|
a1i |
|
120 |
119
|
rpgt0d |
|
121 |
30 32 120 66
|
mulgt0d |
|
122 |
33 71 121
|
3jca |
|
123 |
|
expgt0 |
|
124 |
122 123
|
syl |
|
125 |
49 72 124
|
ltled |
|
126 |
72 119 125
|
divge0d |
|
127 |
116 47
|
resubcld |
|
128 |
48 54
|
elrpd |
|
129 |
116
|
lem1d |
|
130 |
127 116 128 129
|
lediv1dd |
|
131 |
115 117 73 126 130
|
lemul2ad |
|
132 |
48
|
recnd |
|
133 |
110 132 57
|
divrecd |
|
134 |
133
|
oveq2d |
|
135 |
58
|
recnd |
|
136 |
74 110 135
|
mulassd |
|
137 |
136
|
eqcomd |
|
138 |
86 110 62 45
|
div23d |
|
139 |
138
|
eqcomd |
|
140 |
88 70
|
jca |
|
141 |
35
|
recnd |
|
142 |
5 8 9
|
knoppndvlem13 |
|
143 |
34 142
|
absne0d |
|
144 |
141 143
|
jca |
|
145 |
140 144 11
|
3jca |
|
146 |
|
mulexpz |
|
147 |
145 146
|
syl |
|
148 |
147
|
oveq2d |
|
149 |
88 6
|
expcld |
|
150 |
43
|
recnd |
|
151 |
86 149 150
|
mulassd |
|
152 |
151
|
eqcomd |
|
153 |
140 71 11
|
jca32 |
|
154 |
|
expaddz |
|
155 |
153 154
|
syl |
|
156 |
155
|
eqcomd |
|
157 |
71
|
zcnd |
|
158 |
6
|
nn0cnd |
|
159 |
157 158
|
addcomd |
|
160 |
158
|
negidd |
|
161 |
159 160
|
eqtrd |
|
162 |
161
|
oveq2d |
|
163 |
88
|
exp0d |
|
164 |
156 162 163
|
3eqtrd |
|
165 |
164
|
oveq1d |
|
166 |
150
|
mulid2d |
|
167 |
165 166
|
eqtrd |
|
168 |
148 152 167
|
3eqtrd |
|
169 |
168
|
oveq1d |
|
170 |
139 169
|
eqtrd |
|
171 |
170
|
oveq1d |
|
172 |
134 137 171
|
3eqtrd |
|
173 |
131 172
|
breqtrd |
|
174 |
114 173
|
eqbrtrd |
|
175 |
24 42 59 60 174
|
letrd |
|