Step |
Hyp |
Ref |
Expression |
1 |
|
poimir.0 |
|
2 |
|
poimirlem2.1 |
|
3 |
|
poimirlem2.2 |
|
4 |
|
poimirlem2.3 |
|
5 |
|
poimirlem1.4 |
|
6 |
|
f1of |
|
7 |
4 6
|
syl |
|
8 |
1
|
nncnd |
|
9 |
|
npcan1 |
|
10 |
8 9
|
syl |
|
11 |
1
|
nnzd |
|
12 |
|
peano2zm |
|
13 |
|
uzid |
|
14 |
|
peano2uz |
|
15 |
11 12 13 14
|
4syl |
|
16 |
10 15
|
eqeltrrd |
|
17 |
|
fzss2 |
|
18 |
16 17
|
syl |
|
19 |
18 5
|
sseldd |
|
20 |
7 19
|
ffvelrnd |
|
21 |
|
fzp1elp1 |
|
22 |
5 21
|
syl |
|
23 |
10
|
oveq2d |
|
24 |
22 23
|
eleqtrd |
|
25 |
7 24
|
ffvelrnd |
|
26 |
|
imassrn |
|
27 |
|
frn |
|
28 |
4 6 27
|
3syl |
|
29 |
26 28
|
sstrid |
|
30 |
29
|
sselda |
|
31 |
3
|
ffvelrnda |
|
32 |
31
|
zred |
|
33 |
32
|
ltp1d |
|
34 |
32 33
|
ltned |
|
35 |
30 34
|
syldan |
|
36 |
|
breq1 |
|
37 |
|
id |
|
38 |
36 37
|
ifbieq1d |
|
39 |
|
elfzelz |
|
40 |
5 39
|
syl |
|
41 |
40
|
zred |
|
42 |
41
|
ltm1d |
|
43 |
42
|
iftrued |
|
44 |
38 43
|
sylan9eqr |
|
45 |
44
|
csbeq1d |
|
46 |
11 12
|
syl |
|
47 |
|
elfzm1b |
|
48 |
40 46 47
|
syl2anc |
|
49 |
5 48
|
mpbid |
|
50 |
|
oveq2 |
|
51 |
50
|
imaeq2d |
|
52 |
51
|
xpeq1d |
|
53 |
52
|
adantl |
|
54 |
|
oveq1 |
|
55 |
40
|
zcnd |
|
56 |
|
npcan1 |
|
57 |
55 56
|
syl |
|
58 |
54 57
|
sylan9eqr |
|
59 |
58
|
oveq1d |
|
60 |
59
|
imaeq2d |
|
61 |
60
|
xpeq1d |
|
62 |
53 61
|
uneq12d |
|
63 |
62
|
oveq2d |
|
64 |
49 63
|
csbied |
|
65 |
64
|
adantr |
|
66 |
45 65
|
eqtrd |
|
67 |
46
|
zcnd |
|
68 |
|
npcan1 |
|
69 |
67 68
|
syl |
|
70 |
|
peano2zm |
|
71 |
|
uzid |
|
72 |
|
peano2uz |
|
73 |
46 70 71 72
|
4syl |
|
74 |
69 73
|
eqeltrrd |
|
75 |
|
fzss2 |
|
76 |
74 75
|
syl |
|
77 |
76 49
|
sseldd |
|
78 |
|
ovexd |
|
79 |
2 66 77 78
|
fvmptd |
|
80 |
79
|
fveq1d |
|
81 |
80
|
adantr |
|
82 |
3
|
ffnd |
|
83 |
82
|
adantr |
|
84 |
|
1ex |
|
85 |
|
fnconstg |
|
86 |
84 85
|
ax-mp |
|
87 |
|
c0ex |
|
88 |
|
fnconstg |
|
89 |
87 88
|
ax-mp |
|
90 |
86 89
|
pm3.2i |
|
91 |
|
dff1o3 |
|
92 |
91
|
simprbi |
|
93 |
|
imain |
|
94 |
4 92 93
|
3syl |
|
95 |
|
fzdisj |
|
96 |
42 95
|
syl |
|
97 |
96
|
imaeq2d |
|
98 |
|
ima0 |
|
99 |
97 98
|
eqtrdi |
|
100 |
94 99
|
eqtr3d |
|
101 |
|
fnun |
|
102 |
90 100 101
|
sylancr |
|
103 |
|
elfzuz |
|
104 |
5 103
|
syl |
|
105 |
57 104
|
eqeltrd |
|
106 |
|
peano2zm |
|
107 |
|
uzid |
|
108 |
|
peano2uz |
|
109 |
40 106 107 108
|
4syl |
|
110 |
57 109
|
eqeltrrd |
|
111 |
|
peano2uz |
|
112 |
|
uzss |
|
113 |
110 111 112
|
3syl |
|
114 |
|
elfzuz3 |
|
115 |
|
eluzp1p1 |
|
116 |
5 114 115
|
3syl |
|
117 |
10 116
|
eqeltrrd |
|
118 |
113 117
|
sseldd |
|
119 |
|
fzsplit2 |
|
120 |
105 118 119
|
syl2anc |
|
121 |
57
|
oveq1d |
|
122 |
121
|
uneq2d |
|
123 |
120 122
|
eqtrd |
|
124 |
123
|
imaeq2d |
|
125 |
|
imaundi |
|
126 |
124 125
|
eqtrdi |
|
127 |
|
f1ofo |
|
128 |
|
foima |
|
129 |
4 127 128
|
3syl |
|
130 |
126 129
|
eqtr3d |
|
131 |
130
|
fneq2d |
|
132 |
102 131
|
mpbid |
|
133 |
132
|
adantr |
|
134 |
|
ovexd |
|
135 |
|
inidm |
|
136 |
|
eqidd |
|
137 |
100
|
adantr |
|
138 |
|
fzss2 |
|
139 |
|
imass2 |
|
140 |
117 138 139
|
3syl |
|
141 |
140
|
sselda |
|
142 |
|
fvun2 |
|
143 |
86 89 142
|
mp3an12 |
|
144 |
137 141 143
|
syl2anc |
|
145 |
87
|
fvconst2 |
|
146 |
141 145
|
syl |
|
147 |
144 146
|
eqtrd |
|
148 |
147
|
adantr |
|
149 |
83 133 134 134 135 136 148
|
ofval |
|
150 |
30 149
|
mpdan |
|
151 |
31
|
zcnd |
|
152 |
151
|
addid1d |
|
153 |
30 152
|
syldan |
|
154 |
81 150 153
|
3eqtrd |
|
155 |
|
breq1 |
|
156 |
|
oveq1 |
|
157 |
155 156
|
ifbieq2d |
|
158 |
41
|
ltnrd |
|
159 |
158
|
iffalsed |
|
160 |
157 159
|
sylan9eqr |
|
161 |
160
|
csbeq1d |
|
162 |
|
ovex |
|
163 |
|
oveq2 |
|
164 |
163
|
imaeq2d |
|
165 |
164
|
xpeq1d |
|
166 |
|
oveq1 |
|
167 |
166
|
oveq1d |
|
168 |
167
|
imaeq2d |
|
169 |
168
|
xpeq1d |
|
170 |
165 169
|
uneq12d |
|
171 |
170
|
oveq2d |
|
172 |
162 171
|
csbie |
|
173 |
161 172
|
eqtrdi |
|
174 |
|
fz1ssfz0 |
|
175 |
174 5
|
sseldi |
|
176 |
|
ovexd |
|
177 |
2 173 175 176
|
fvmptd |
|
178 |
177
|
fveq1d |
|
179 |
178
|
adantr |
|
180 |
|
fnconstg |
|
181 |
84 180
|
ax-mp |
|
182 |
|
fnconstg |
|
183 |
87 182
|
ax-mp |
|
184 |
181 183
|
pm3.2i |
|
185 |
|
imain |
|
186 |
4 92 185
|
3syl |
|
187 |
|
peano2re |
|
188 |
41 187
|
syl |
|
189 |
188
|
ltp1d |
|
190 |
|
fzdisj |
|
191 |
189 190
|
syl |
|
192 |
191
|
imaeq2d |
|
193 |
186 192
|
eqtr3d |
|
194 |
193 98
|
eqtrdi |
|
195 |
|
fnun |
|
196 |
184 194 195
|
sylancr |
|
197 |
|
fzsplit |
|
198 |
24 197
|
syl |
|
199 |
198
|
imaeq2d |
|
200 |
|
imaundi |
|
201 |
199 200
|
eqtrdi |
|
202 |
201 129
|
eqtr3d |
|
203 |
202
|
fneq2d |
|
204 |
196 203
|
mpbid |
|
205 |
204
|
adantr |
|
206 |
194
|
adantr |
|
207 |
|
fzss1 |
|
208 |
|
imass2 |
|
209 |
104 207 208
|
3syl |
|
210 |
209
|
sselda |
|
211 |
|
fvun1 |
|
212 |
181 183 211
|
mp3an12 |
|
213 |
206 210 212
|
syl2anc |
|
214 |
84
|
fvconst2 |
|
215 |
210 214
|
syl |
|
216 |
213 215
|
eqtrd |
|
217 |
216
|
adantr |
|
218 |
83 205 134 134 135 136 217
|
ofval |
|
219 |
30 218
|
mpdan |
|
220 |
179 219
|
eqtrd |
|
221 |
35 154 220
|
3netr4d |
|
222 |
221
|
ralrimiva |
|
223 |
|
fzpr |
|
224 |
5 39 223
|
3syl |
|
225 |
224
|
imaeq2d |
|
226 |
|
f1ofn |
|
227 |
4 226
|
syl |
|
228 |
|
fnimapr |
|
229 |
227 19 24 228
|
syl3anc |
|
230 |
225 229
|
eqtrd |
|
231 |
230
|
raleqdv |
|
232 |
222 231
|
mpbid |
|
233 |
|
fvex |
|
234 |
|
fvex |
|
235 |
|
fveq2 |
|
236 |
|
fveq2 |
|
237 |
235 236
|
neeq12d |
|
238 |
|
fveq2 |
|
239 |
|
fveq2 |
|
240 |
238 239
|
neeq12d |
|
241 |
233 234 237 240
|
ralpr |
|
242 |
232 241
|
sylib |
|
243 |
41
|
ltp1d |
|
244 |
41 243
|
ltned |
|
245 |
|
f1of1 |
|
246 |
4 245
|
syl |
|
247 |
|
f1veqaeq |
|
248 |
246 19 24 247
|
syl12anc |
|
249 |
248
|
necon3d |
|
250 |
244 249
|
mpd |
|
251 |
237
|
anbi1d |
|
252 |
|
neeq1 |
|
253 |
251 252
|
anbi12d |
|
254 |
|
fveq2 |
|
255 |
|
fveq2 |
|
256 |
254 255
|
neeq12d |
|
257 |
256
|
anbi2d |
|
258 |
|
neeq2 |
|
259 |
257 258
|
anbi12d |
|
260 |
253 259
|
rspc2ev |
|
261 |
20 25 242 250 260
|
syl112anc |
|
262 |
|
dfrex2 |
|
263 |
|
fveq2 |
|
264 |
|
fveq2 |
|
265 |
263 264
|
neeq12d |
|
266 |
265
|
rmo4 |
|
267 |
|
dfral2 |
|
268 |
|
df-ne |
|
269 |
268
|
anbi2i |
|
270 |
|
annim |
|
271 |
269 270
|
bitri |
|
272 |
271
|
rexbii |
|
273 |
267 272
|
xchbinxr |
|
274 |
273
|
ralbii |
|
275 |
266 274
|
bitri |
|
276 |
262 275
|
xchbinxr |
|
277 |
261 276
|
sylib |
|