Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
|
1z |
|
3 |
|
seq1 |
|
4 |
2 3
|
ax-mp |
|
5 |
1 4
|
eqtrdi |
|
6 |
|
oveq1 |
|
7 |
|
oveq1 |
|
8 |
6 7
|
oveq12d |
|
9 |
8
|
oveq2d |
|
10 |
5 9
|
eqeq12d |
|
11 |
10
|
imbi2d |
|
12 |
|
fveq2 |
|
13 |
|
oveq1 |
|
14 |
|
oveq1 |
|
15 |
13 14
|
oveq12d |
|
16 |
15
|
oveq2d |
|
17 |
12 16
|
eqeq12d |
|
18 |
17
|
imbi2d |
|
19 |
|
fveq2 |
|
20 |
|
oveq1 |
|
21 |
|
oveq1 |
|
22 |
20 21
|
oveq12d |
|
23 |
22
|
oveq2d |
|
24 |
19 23
|
eqeq12d |
|
25 |
24
|
imbi2d |
|
26 |
|
fveq2 |
|
27 |
|
oveq1 |
|
28 |
|
oveq1 |
|
29 |
27 28
|
oveq12d |
|
30 |
29
|
oveq2d |
|
31 |
26 30
|
eqeq12d |
|
32 |
31
|
imbi2d |
|
33 |
|
1nn |
|
34 |
|
oveq2 |
|
35 |
34
|
oveq2d |
|
36 |
|
oveq2 |
|
37 |
36
|
oveq2d |
|
38 |
35 37
|
oveq12d |
|
39 |
|
oveq2 |
|
40 |
39
|
oveq2d |
|
41 |
38 40
|
oveq12d |
|
42 |
|
eqid |
|
43 |
|
ovex |
|
44 |
41 42 43
|
fvmpt |
|
45 |
33 44
|
ax-mp |
|
46 |
|
nn0cn |
|
47 |
46
|
div1d |
|
48 |
47
|
oveq2d |
|
49 |
|
1div1e1 |
|
50 |
49
|
oveq2i |
|
51 |
50
|
a1i |
|
52 |
48 51
|
oveq12d |
|
53 |
|
nn0p1nn |
|
54 |
53
|
nncnd |
|
55 |
54
|
div1d |
|
56 |
55
|
oveq2d |
|
57 |
52 56
|
oveq12d |
|
58 |
|
1cnd |
|
59 |
58 46
|
addcomd |
|
60 |
59
|
oveq1d |
|
61 |
60
|
oveq1d |
|
62 |
|
ax-1cn |
|
63 |
62 62
|
addcli |
|
64 |
63
|
a1i |
|
65 |
33
|
a1i |
|
66 |
65 53
|
nnaddcld |
|
67 |
66
|
nncnd |
|
68 |
66
|
nnne0d |
|
69 |
54 64 67 68
|
divassd |
|
70 |
57 61 69
|
3eqtrd |
|
71 |
45 70
|
syl5eq |
|
72 |
|
seqp1 |
|
73 |
|
nnuz |
|
74 |
72 73
|
eleq2s |
|
75 |
74
|
adantr |
|
76 |
75
|
adantr |
|
77 |
|
oveq1 |
|
78 |
77
|
adantl |
|
79 |
|
peano2nn |
|
80 |
|
oveq2 |
|
81 |
80
|
oveq2d |
|
82 |
|
oveq2 |
|
83 |
82
|
oveq2d |
|
84 |
81 83
|
oveq12d |
|
85 |
|
oveq2 |
|
86 |
85
|
oveq2d |
|
87 |
84 86
|
oveq12d |
|
88 |
|
ovex |
|
89 |
87 42 88
|
fvmpt |
|
90 |
79 89
|
syl |
|
91 |
90
|
oveq2d |
|
92 |
91
|
adantr |
|
93 |
53
|
adantl |
|
94 |
93
|
nncnd |
|
95 |
79
|
adantr |
|
96 |
95
|
nnrpd |
|
97 |
|
simpl |
|
98 |
97
|
nnrpd |
|
99 |
93
|
nnrpd |
|
100 |
98 99
|
rpaddcld |
|
101 |
96 100
|
rpdivcld |
|
102 |
101
|
rpcnd |
|
103 |
|
1cnd |
|
104 |
|
nn0re |
|
105 |
104
|
adantl |
|
106 |
105 95
|
nndivred |
|
107 |
106
|
recnd |
|
108 |
103 107
|
addcomd |
|
109 |
|
nn0ge0 |
|
110 |
109
|
adantl |
|
111 |
105 96 110
|
divge0d |
|
112 |
106 111
|
ge0p1rpd |
|
113 |
108 112
|
eqeltrd |
|
114 |
|
1rp |
|
115 |
114
|
a1i |
|
116 |
96
|
rpreccld |
|
117 |
115 116
|
rpaddcld |
|
118 |
113 117
|
rpmulcld |
|
119 |
99 96
|
rpdivcld |
|
120 |
115 119
|
rpaddcld |
|
121 |
118 120
|
rpdivcld |
|
122 |
121
|
rpcnd |
|
123 |
94 102 122
|
mulassd |
|
124 |
101 118
|
rpmulcld |
|
125 |
124
|
rpcnd |
|
126 |
120
|
rpcnd |
|
127 |
95
|
nncnd |
|
128 |
120
|
rpne0d |
|
129 |
95
|
nnne0d |
|
130 |
125 126 127 128 129
|
divcan5d |
|
131 |
118
|
rpcnd |
|
132 |
127 102 131
|
mul12d |
|
133 |
113
|
rpcnd |
|
134 |
117
|
rpcnd |
|
135 |
127 133 134
|
mulassd |
|
136 |
127 103 107
|
adddid |
|
137 |
127
|
mulid1d |
|
138 |
|
simpr |
|
139 |
138
|
nn0cnd |
|
140 |
139 127 129
|
divcan2d |
|
141 |
137 140
|
oveq12d |
|
142 |
97
|
nncnd |
|
143 |
142 103 139
|
addassd |
|
144 |
103 139
|
addcomd |
|
145 |
144
|
oveq2d |
|
146 |
143 145
|
eqtrd |
|
147 |
136 141 146
|
3eqtrd |
|
148 |
147
|
oveq1d |
|
149 |
135 148
|
eqtr3d |
|
150 |
149
|
oveq2d |
|
151 |
100
|
rpcnd |
|
152 |
102 151 134
|
mulassd |
|
153 |
100
|
rpne0d |
|
154 |
127 151 153
|
divcan1d |
|
155 |
154
|
oveq1d |
|
156 |
116
|
rpcnd |
|
157 |
127 103 156
|
adddid |
|
158 |
103 127 129
|
divcan2d |
|
159 |
137 158
|
oveq12d |
|
160 |
155 157 159
|
3eqtrd |
|
161 |
152 160
|
eqtr3d |
|
162 |
132 150 161
|
3eqtrd |
|
163 |
119
|
rpcnd |
|
164 |
127 103 163
|
adddid |
|
165 |
94 127 129
|
divcan2d |
|
166 |
137 165
|
oveq12d |
|
167 |
164 166
|
eqtrd |
|
168 |
162 167
|
oveq12d |
|
169 |
102 131 126 128
|
divassd |
|
170 |
130 168 169
|
3eqtr3rd |
|
171 |
170
|
oveq2d |
|
172 |
92 123 171
|
3eqtrd |
|
173 |
172
|
adantr |
|
174 |
76 78 173
|
3eqtrd |
|
175 |
174
|
exp31 |
|
176 |
175
|
a2d |
|
177 |
11 18 25 32 71 176
|
nnind |
|
178 |
177
|
impcom |
|
179 |
|
oveq1 |
|
180 |
|
oveq1 |
|
181 |
179 180
|
oveq12d |
|
182 |
181
|
oveq2d |
|
183 |
|
eqid |
|
184 |
|
ovex |
|
185 |
182 183 184
|
fvmpt |
|
186 |
185
|
adantl |
|
187 |
178 186
|
eqtr4d |
|
188 |
187
|
ralrimiva |
|
189 |
|
seqfn |
|
190 |
2 189
|
ax-mp |
|
191 |
73
|
fneq2i |
|
192 |
190 191
|
mpbir |
|
193 |
|
ovex |
|
194 |
193 183
|
fnmpti |
|
195 |
|
eqfnfv |
|
196 |
192 194 195
|
mp2an |
|
197 |
188 196
|
sylibr |
|