Step |
Hyp |
Ref |
Expression |
1 |
|
circlemeth.n |
|
2 |
|
circlemeth.s |
|
3 |
|
circlemeth.l |
|
4 |
1
|
adantr |
|
5 |
|
ioossre |
|
6 |
|
ax-resscn |
|
7 |
5 6
|
sstri |
|
8 |
7
|
a1i |
|
9 |
8
|
sselda |
|
10 |
2
|
nnnn0d |
|
11 |
10
|
adantr |
|
12 |
3
|
adantr |
|
13 |
4 9 11 12
|
vtsprod |
|
14 |
13
|
oveq1d |
|
15 |
|
fzfid |
|
16 |
|
ax-icn |
|
17 |
|
2cn |
|
18 |
|
picn |
|
19 |
17 18
|
mulcli |
|
20 |
16 19
|
mulcli |
|
21 |
20
|
a1i |
|
22 |
1
|
nn0cnd |
|
23 |
22
|
negcld |
|
24 |
23
|
ralrimivw |
|
25 |
24
|
r19.21bi |
|
26 |
25 9
|
mulcld |
|
27 |
21 26
|
mulcld |
|
28 |
27
|
efcld |
|
29 |
|
fz1ssnn |
|
30 |
29
|
a1i |
|
31 |
|
fzssz |
|
32 |
|
simpr |
|
33 |
31 32
|
sseldi |
|
34 |
33
|
adantlr |
|
35 |
11
|
adantr |
|
36 |
|
fzfid |
|
37 |
30 34 35 36
|
reprfi |
|
38 |
|
fzofi |
|
39 |
38
|
a1i |
|
40 |
1
|
ad3antrrr |
|
41 |
10
|
ad3antrrr |
|
42 |
33
|
zcnd |
|
43 |
42
|
ad2antrr |
|
44 |
3
|
ad3antrrr |
|
45 |
|
simpr |
|
46 |
29
|
a1i |
|
47 |
33
|
adantr |
|
48 |
10
|
ad2antrr |
|
49 |
|
simpr |
|
50 |
46 47 48 49
|
reprf |
|
51 |
50
|
ffvelrnda |
|
52 |
29 51
|
sseldi |
|
53 |
40 41 43 44 45 52
|
breprexplemb |
|
54 |
53
|
adantl3r |
|
55 |
39 54
|
fprodcl |
|
56 |
20
|
a1i |
|
57 |
34
|
zcnd |
|
58 |
9
|
adantr |
|
59 |
57 58
|
mulcld |
|
60 |
56 59
|
mulcld |
|
61 |
60
|
efcld |
|
62 |
61
|
adantr |
|
63 |
55 62
|
mulcld |
|
64 |
37 63
|
fsumcl |
|
65 |
15 28 64
|
fsummulc1 |
|
66 |
28
|
adantr |
|
67 |
37 66 63
|
fsummulc1 |
|
68 |
66
|
adantr |
|
69 |
55 62 68
|
mulassd |
|
70 |
27
|
adantr |
|
71 |
|
efadd |
|
72 |
60 70 71
|
syl2anc |
|
73 |
26
|
adantr |
|
74 |
56 59 73
|
adddid |
|
75 |
25
|
adantr |
|
76 |
57 75 58
|
adddird |
|
77 |
22
|
ad2antrr |
|
78 |
57 77
|
negsubd |
|
79 |
78
|
oveq1d |
|
80 |
76 79
|
eqtr3d |
|
81 |
80
|
oveq2d |
|
82 |
74 81
|
eqtr3d |
|
83 |
82
|
fveq2d |
|
84 |
72 83
|
eqtr3d |
|
85 |
84
|
oveq2d |
|
86 |
85
|
adantr |
|
87 |
69 86
|
eqtrd |
|
88 |
87
|
sumeq2dv |
|
89 |
67 88
|
eqtrd |
|
90 |
89
|
sumeq2dv |
|
91 |
14 65 90
|
3eqtrd |
|
92 |
91
|
itgeq2dv |
|
93 |
|
ioombl |
|
94 |
93
|
a1i |
|
95 |
|
fzfid |
|
96 |
|
sumex |
|
97 |
96
|
a1i |
|
98 |
94
|
adantr |
|
99 |
29
|
a1i |
|
100 |
10
|
adantr |
|
101 |
|
fzfid |
|
102 |
99 33 100 101
|
reprfi |
|
103 |
38
|
a1i |
|
104 |
53
|
adantllr |
|
105 |
103 104
|
fprodcl |
|
106 |
57 77
|
subcld |
|
107 |
106 58
|
mulcld |
|
108 |
56 107
|
mulcld |
|
109 |
108
|
an32s |
|
110 |
109
|
adantr |
|
111 |
110
|
efcld |
|
112 |
105 111
|
mulcld |
|
113 |
112
|
anasss |
|
114 |
38
|
a1i |
|
115 |
114 53
|
fprodcl |
|
116 |
|
fvex |
|
117 |
116
|
a1i |
|
118 |
|
ioossicc |
|
119 |
118
|
a1i |
|
120 |
93
|
a1i |
|
121 |
116
|
a1i |
|
122 |
|
0red |
|
123 |
|
1red |
|
124 |
22
|
adantr |
|
125 |
42 124
|
subcld |
|
126 |
|
unitsscn |
|
127 |
126
|
a1i |
|
128 |
|
ssidd |
|
129 |
|
cncfmptc |
|
130 |
125 127 128 129
|
syl3anc |
|
131 |
|
cncfmptid |
|
132 |
127 128 131
|
syl2anc |
|
133 |
130 132
|
mulcncf |
|
134 |
133
|
efmul2picn |
|
135 |
|
cniccibl |
|
136 |
122 123 134 135
|
syl3anc |
|
137 |
119 120 121 136
|
iblss |
|
138 |
137
|
adantr |
|
139 |
115 117 138
|
iblmulc2 |
|
140 |
98 102 113 139
|
itgfsum |
|
141 |
140
|
simpld |
|
142 |
94 95 97 141
|
itgfsum |
|
143 |
142
|
simprd |
|
144 |
|
oveq2 |
|
145 |
|
oveq2 |
|
146 |
102 115
|
fsumcl |
|
147 |
146
|
mulid1d |
|
148 |
146
|
mul01d |
|
149 |
144 145 147 148
|
ifeq3da |
|
150 |
|
velsn |
|
151 |
42 124
|
subeq0ad |
|
152 |
150 151
|
bitr4id |
|
153 |
152
|
ifbid |
|
154 |
1
|
nn0zd |
|
155 |
154
|
ad2antrr |
|
156 |
47 155
|
zsubcld |
|
157 |
|
itgexpif |
|
158 |
156 157
|
syl |
|
159 |
158
|
oveq2d |
|
160 |
159
|
sumeq2dv |
|
161 |
|
1cnd |
|
162 |
|
0cnd |
|
163 |
161 162
|
ifcld |
|
164 |
102 163 115
|
fsummulc1 |
|
165 |
160 164
|
eqtr4d |
|
166 |
149 153 165
|
3eqtr4rd |
|
167 |
166
|
sumeq2dv |
|
168 |
|
0zd |
|
169 |
10
|
nn0zd |
|
170 |
169 154
|
zmulcld |
|
171 |
1
|
nn0ge0d |
|
172 |
|
nnmulge |
|
173 |
2 1 172
|
syl2anc |
|
174 |
|
elfz4 |
|
175 |
168 170 154 171 173 174
|
syl32anc |
|
176 |
175
|
snssd |
|
177 |
176
|
sselda |
|
178 |
177 146
|
syldan |
|
179 |
178
|
ralrimiva |
|
180 |
95
|
olcd |
|
181 |
|
sumss2 |
|
182 |
176 179 180 181
|
syl21anc |
|
183 |
29
|
a1i |
|
184 |
|
fzfid |
|
185 |
183 154 10 184
|
reprfi |
|
186 |
38
|
a1i |
|
187 |
1
|
ad2antrr |
|
188 |
10
|
ad2antrr |
|
189 |
22
|
ad2antrr |
|
190 |
3
|
ad2antrr |
|
191 |
|
simpr |
|
192 |
29
|
a1i |
|
193 |
154
|
adantr |
|
194 |
10
|
adantr |
|
195 |
|
simpr |
|
196 |
192 193 194 195
|
reprf |
|
197 |
196
|
ffvelrnda |
|
198 |
29 197
|
sseldi |
|
199 |
187 188 189 190 191 198
|
breprexplemb |
|
200 |
186 199
|
fprodcl |
|
201 |
185 200
|
fsumcl |
|
202 |
|
oveq2 |
|
203 |
202
|
sumeq1d |
|
204 |
203
|
sumsn |
|
205 |
1 201 204
|
syl2anc |
|
206 |
167 182 205
|
3eqtr2d |
|
207 |
140
|
simprd |
|
208 |
111
|
an32s |
|
209 |
115 208 138
|
itgmulc2 |
|
210 |
209
|
sumeq2dv |
|
211 |
207 210
|
eqtr4d |
|
212 |
211
|
sumeq2dv |
|
213 |
1 10
|
reprfz1 |
|
214 |
213
|
sumeq1d |
|
215 |
206 212 214
|
3eqtr4d |
|
216 |
92 143 215
|
3eqtrrd |
|