Step |
Hyp |
Ref |
Expression |
1 |
|
yoneda.y |
|
2 |
|
yoneda.b |
|
3 |
|
yoneda.1 |
|
4 |
|
yoneda.o |
|
5 |
|
yoneda.s |
|
6 |
|
yoneda.t |
|
7 |
|
yoneda.q |
|
8 |
|
yoneda.h |
|
9 |
|
yoneda.r |
|
10 |
|
yoneda.e |
|
11 |
|
yoneda.z |
|
12 |
|
yoneda.c |
|
13 |
|
yoneda.w |
|
14 |
|
yoneda.u |
|
15 |
|
yoneda.v |
|
16 |
|
yonedalem21.f |
|
17 |
|
yonedalem21.x |
|
18 |
|
yonedalem22.g |
|
19 |
|
yonedalem22.p |
|
20 |
|
yonedalem22.a |
|
21 |
|
yonedalem22.k |
|
22 |
|
yonedalem3.m |
|
23 |
|
oveq2 |
|
24 |
23
|
oveq1d |
|
25 |
24
|
fveq1d |
|
26 |
25
|
fveq1d |
|
27 |
26
|
cbvmptv |
|
28 |
|
eqid |
|
29 |
4 2
|
oppcbas |
|
30 |
|
eqid |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
7 28
|
fuchom |
|
34 |
|
relfunc |
|
35 |
15
|
unssbd |
|
36 |
13 35
|
ssexd |
|
37 |
1 12 4 5 7 36 14
|
yoncl |
|
38 |
|
1st2ndbr |
|
39 |
34 37 38
|
sylancr |
|
40 |
2 32 33 39 19 17
|
funcf2 |
|
41 |
40 21
|
ffvelrnd |
|
42 |
41
|
adantr |
|
43 |
|
simpr |
|
44 |
20
|
adantr |
|
45 |
7 28 31 43 44
|
fuccocl |
|
46 |
19
|
adantr |
|
47 |
7 28 29 30 31 42 45 46
|
fuccoval |
|
48 |
7 28 29 30 31 43 44 46
|
fuccoval |
|
49 |
36
|
adantr |
|
50 |
|
eqid |
|
51 |
|
relfunc |
|
52 |
7
|
fucbas |
|
53 |
2 52 39
|
funcf1 |
|
54 |
53 17
|
ffvelrnd |
|
55 |
|
1st2ndbr |
|
56 |
51 54 55
|
sylancr |
|
57 |
29 50 56
|
funcf1 |
|
58 |
5 36
|
setcbas |
|
59 |
58
|
feq3d |
|
60 |
57 59
|
mpbird |
|
61 |
60 19
|
ffvelrnd |
|
62 |
61
|
adantr |
|
63 |
|
1st2ndbr |
|
64 |
51 16 63
|
sylancr |
|
65 |
29 50 64
|
funcf1 |
|
66 |
58
|
feq3d |
|
67 |
65 66
|
mpbird |
|
68 |
67 19
|
ffvelrnd |
|
69 |
68
|
adantr |
|
70 |
|
1st2ndbr |
|
71 |
51 18 70
|
sylancr |
|
72 |
29 50 71
|
funcf1 |
|
73 |
72 19
|
ffvelrnd |
|
74 |
73 58
|
eleqtrrd |
|
75 |
74
|
adantr |
|
76 |
28 43
|
nat1st2nd |
|
77 |
|
eqid |
|
78 |
28 76 29 77 46
|
natcl |
|
79 |
5 49 77 62 69
|
elsetchom |
|
80 |
78 79
|
mpbid |
|
81 |
28 20
|
nat1st2nd |
|
82 |
28 81 29 77 19
|
natcl |
|
83 |
5 36 77 68 74
|
elsetchom |
|
84 |
82 83
|
mpbid |
|
85 |
84
|
adantr |
|
86 |
5 49 30 62 69 75 80 85
|
setcco |
|
87 |
48 86
|
eqtrd |
|
88 |
87
|
oveq1d |
|
89 |
53 19
|
ffvelrnd |
|
90 |
|
1st2ndbr |
|
91 |
51 89 90
|
sylancr |
|
92 |
29 50 91
|
funcf1 |
|
93 |
92 19
|
ffvelrnd |
|
94 |
93 58
|
eleqtrrd |
|
95 |
94
|
adantr |
|
96 |
28 41
|
nat1st2nd |
|
97 |
28 96 29 77 19
|
natcl |
|
98 |
5 36 77 94 61
|
elsetchom |
|
99 |
97 98
|
mpbid |
|
100 |
99
|
adantr |
|
101 |
|
fco |
|
102 |
85 80 101
|
syl2anc |
|
103 |
5 49 30 95 62 75 100 102
|
setcco |
|
104 |
47 88 103
|
3eqtrd |
|
105 |
104
|
fveq1d |
|
106 |
2 32 3 12 19
|
catidcl |
|
107 |
1 2 12 19 32 19
|
yon11 |
|
108 |
106 107
|
eleqtrrd |
|
109 |
108
|
adantr |
|
110 |
|
fvco3 |
|
111 |
100 109 110
|
syl2anc |
|
112 |
100 109
|
ffvelrnd |
|
113 |
|
fvco3 |
|
114 |
80 112 113
|
syl2anc |
|
115 |
12
|
adantr |
|
116 |
17
|
adantr |
|
117 |
|
eqid |
|
118 |
21
|
adantr |
|
119 |
106
|
adantr |
|
120 |
1 2 115 46 32 116 117 46 118 119
|
yon2 |
|
121 |
2 32 3 115 46 117 116 118
|
catrid |
|
122 |
120 121
|
eqtrd |
|
123 |
122
|
fveq2d |
|
124 |
|
eqid |
|
125 |
29 124 77 56 17 19
|
funcf2 |
|
126 |
32 4
|
oppchom |
|
127 |
21 126
|
eleqtrrdi |
|
128 |
125 127
|
ffvelrnd |
|
129 |
60 17
|
ffvelrnd |
|
130 |
5 36 77 129 61
|
elsetchom |
|
131 |
128 130
|
mpbid |
|
132 |
131
|
adantr |
|
133 |
2 32 3 12 17
|
catidcl |
|
134 |
1 2 12 17 32 17
|
yon11 |
|
135 |
133 134
|
eleqtrrd |
|
136 |
135
|
adantr |
|
137 |
|
fvco3 |
|
138 |
132 136 137
|
syl2anc |
|
139 |
127
|
adantr |
|
140 |
28 76 29 124 30 116 46 139
|
nati |
|
141 |
129
|
adantr |
|
142 |
5 49 30 141 62 69 132 80
|
setcco |
|
143 |
67 17
|
ffvelrnd |
|
144 |
143
|
adantr |
|
145 |
28 76 29 77 116
|
natcl |
|
146 |
5 49 77 141 144
|
elsetchom |
|
147 |
145 146
|
mpbid |
|
148 |
29 124 77 64 17 19
|
funcf2 |
|
149 |
148 127
|
ffvelrnd |
|
150 |
5 36 77 143 68
|
elsetchom |
|
151 |
149 150
|
mpbid |
|
152 |
151
|
adantr |
|
153 |
5 49 30 141 144 69 147 152
|
setcco |
|
154 |
140 142 153
|
3eqtr3d |
|
155 |
154
|
fveq1d |
|
156 |
133
|
adantr |
|
157 |
1 2 115 116 32 116 117 46 118 156
|
yon12 |
|
158 |
2 32 3 115 46 117 116 118
|
catlid |
|
159 |
157 158
|
eqtrd |
|
160 |
159
|
fveq2d |
|
161 |
138 155 160
|
3eqtr3d |
|
162 |
|
fvco3 |
|
163 |
147 136 162
|
syl2anc |
|
164 |
123 161 163
|
3eqtr2d |
|
165 |
164
|
fveq2d |
|
166 |
114 165
|
eqtrd |
|
167 |
105 111 166
|
3eqtrd |
|
168 |
167
|
mpteq2dva |
|
169 |
27 168
|
syl5eq |
|
170 |
|
eqid |
|
171 |
170 52 29
|
xpcbas |
|
172 |
|
eqid |
|
173 |
|
eqid |
|
174 |
|
relfunc |
|
175 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
|
yonedalem1 |
|
176 |
175
|
simpld |
|
177 |
|
1st2ndbr |
|
178 |
174 176 177
|
sylancr |
|
179 |
16 17
|
opelxpd |
|
180 |
18 19
|
opelxpd |
|
181 |
171 172 173 178 179 180
|
funcf2 |
|
182 |
170 52 29 33 124 16 17 18 19 172
|
xpchom2 |
|
183 |
126
|
xpeq2i |
|
184 |
182 183
|
eqtrdi |
|
185 |
|
df-ov |
|
186 |
|
df-ov |
|
187 |
185 186
|
oveq12i |
|
188 |
187
|
eqcomi |
|
189 |
188
|
a1i |
|
190 |
184 189
|
feq23d |
|
191 |
181 190
|
mpbid |
|
192 |
191 20 21
|
fovrnd |
|
193 |
|
eqid |
|
194 |
171 193 178
|
funcf1 |
|
195 |
194 16 17
|
fovrnd |
|
196 |
6 13
|
setcbas |
|
197 |
195 196
|
eleqtrrd |
|
198 |
194 18 19
|
fovrnd |
|
199 |
198 196
|
eleqtrrd |
|
200 |
6 13 173 197 199
|
elsetchom |
|
201 |
192 200
|
mpbid |
|
202 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
|
yonedalem22 |
|
203 |
4
|
oppccat |
|
204 |
12 203
|
syl |
|
205 |
5
|
setccat |
|
206 |
36 205
|
syl |
|
207 |
7 204 206
|
fuccat |
|
208 |
8 207 52 33 54 16 89 18 31 41 20
|
hof2val |
|
209 |
202 208
|
eqtrd |
|
210 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
|
yonedalem21 |
|
211 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19
|
yonedalem21 |
|
212 |
209 210 211
|
feq123d |
|
213 |
201 212
|
mpbid |
|
214 |
|
eqid |
|
215 |
214
|
fmpt |
|
216 |
213 215
|
sylibr |
|
217 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 18 19 22
|
yonedalem3a |
|
218 |
217
|
simpld |
|
219 |
|
fveq1 |
|
220 |
219
|
fveq1d |
|
221 |
216 209 218 220
|
fmptcof |
|
222 |
|
eqid |
|
223 |
10 204 206 29 124 30 28 16 18 17 19 222 20 127
|
evlf2val |
|
224 |
5 36 30 143 68 74 151 84
|
setcco |
|
225 |
223 224
|
eqtrd |
|
226 |
225
|
coeq1d |
|
227 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 22
|
yonedalem3a |
|
228 |
227
|
simprd |
|
229 |
227
|
simpld |
|
230 |
10 204 206 29 16 17
|
evlf1 |
|
231 |
229 210 230
|
feq123d |
|
232 |
228 231
|
mpbid |
|
233 |
|
eqid |
|
234 |
233
|
fmpt |
|
235 |
232 234
|
sylibr |
|
236 |
|
fcompt |
|
237 |
84 151 236
|
syl2anc |
|
238 |
|
2fveq3 |
|
239 |
235 229 237 238
|
fmptcof |
|
240 |
226 239
|
eqtrd |
|
241 |
169 221 240
|
3eqtr4d |
|
242 |
|
eqid |
|
243 |
175
|
simprd |
|
244 |
|
1st2ndbr |
|
245 |
174 243 244
|
sylancr |
|
246 |
171 193 245
|
funcf1 |
|
247 |
246 18 19
|
fovrnd |
|
248 |
247 196
|
eleqtrrd |
|
249 |
217
|
simprd |
|
250 |
6 13 242 197 199 248 201 249
|
setcco |
|
251 |
246 16 17
|
fovrnd |
|
252 |
251 196
|
eleqtrrd |
|
253 |
171 172 173 245 179 180
|
funcf2 |
|
254 |
|
df-ov |
|
255 |
|
df-ov |
|
256 |
254 255
|
oveq12i |
|
257 |
256
|
eqcomi |
|
258 |
257
|
a1i |
|
259 |
184 258
|
feq23d |
|
260 |
253 259
|
mpbid |
|
261 |
260 20 21
|
fovrnd |
|
262 |
6 13 173 252 248
|
elsetchom |
|
263 |
261 262
|
mpbid |
|
264 |
6 13 242 197 252 248 228 263
|
setcco |
|
265 |
241 250 264
|
3eqtr4d |
|