Step |
Hyp |
Ref |
Expression |
1 |
|
unieq |
|
2 |
|
uni0 |
|
3 |
1 2
|
eqtrdi |
|
4 |
3
|
ineq2d |
|
5 |
|
in0 |
|
6 |
4 5
|
eqtrdi |
|
7 |
6
|
fveq2d |
|
8 |
|
hash0 |
|
9 |
7 8
|
eqtrdi |
|
10 |
9
|
oveq2d |
|
11 |
|
pweq |
|
12 |
|
pw0 |
|
13 |
11 12
|
eqtrdi |
|
14 |
13
|
sumeq1d |
|
15 |
10 14
|
eqeq12d |
|
16 |
15
|
ralbidv |
|
17 |
|
unieq |
|
18 |
17
|
ineq2d |
|
19 |
18
|
fveq2d |
|
20 |
19
|
oveq2d |
|
21 |
|
pweq |
|
22 |
21
|
sumeq1d |
|
23 |
20 22
|
eqeq12d |
|
24 |
23
|
ralbidv |
|
25 |
|
unieq |
|
26 |
|
uniun |
|
27 |
|
unisnv |
|
28 |
27
|
uneq2i |
|
29 |
26 28
|
eqtri |
|
30 |
25 29
|
eqtrdi |
|
31 |
30
|
ineq2d |
|
32 |
31
|
fveq2d |
|
33 |
32
|
oveq2d |
|
34 |
|
pweq |
|
35 |
34
|
sumeq1d |
|
36 |
33 35
|
eqeq12d |
|
37 |
36
|
ralbidv |
|
38 |
|
unieq |
|
39 |
38
|
ineq2d |
|
40 |
39
|
fveq2d |
|
41 |
40
|
oveq2d |
|
42 |
|
pweq |
|
43 |
42
|
sumeq1d |
|
44 |
41 43
|
eqeq12d |
|
45 |
44
|
ralbidv |
|
46 |
|
hashcl |
|
47 |
46
|
nn0cnd |
|
48 |
47
|
mullidd |
|
49 |
|
0ex |
|
50 |
48 47
|
eqeltrd |
|
51 |
|
fveq2 |
|
52 |
51 8
|
eqtrdi |
|
53 |
52
|
oveq2d |
|
54 |
|
neg1cn |
|
55 |
|
exp0 |
|
56 |
54 55
|
ax-mp |
|
57 |
53 56
|
eqtrdi |
|
58 |
|
rint0 |
|
59 |
58
|
fveq2d |
|
60 |
57 59
|
oveq12d |
|
61 |
60
|
sumsn |
|
62 |
49 50 61
|
sylancr |
|
63 |
47
|
subid1d |
|
64 |
48 62 63
|
3eqtr4rd |
|
65 |
64
|
rgen |
|
66 |
|
fveq2 |
|
67 |
|
ineq1 |
|
68 |
67
|
fveq2d |
|
69 |
66 68
|
oveq12d |
|
70 |
|
simpl |
|
71 |
70
|
ineq1d |
|
72 |
71
|
fveq2d |
|
73 |
72
|
oveq2d |
|
74 |
73
|
sumeq2dv |
|
75 |
69 74
|
eqeq12d |
|
76 |
75
|
rspcva |
|
77 |
76
|
adantll |
|
78 |
|
simpr |
|
79 |
|
inss1 |
|
80 |
|
ssfi |
|
81 |
78 79 80
|
sylancl |
|
82 |
|
fveq2 |
|
83 |
|
ineq1 |
|
84 |
|
in32 |
|
85 |
|
inass |
|
86 |
84 85
|
eqtri |
|
87 |
83 86
|
eqtrdi |
|
88 |
87
|
fveq2d |
|
89 |
82 88
|
oveq12d |
|
90 |
|
ineq1 |
|
91 |
|
in32 |
|
92 |
|
inass |
|
93 |
91 92
|
eqtri |
|
94 |
90 93
|
eqtrdi |
|
95 |
94
|
fveq2d |
|
96 |
95
|
oveq2d |
|
97 |
96
|
sumeq2sdv |
|
98 |
89 97
|
eqeq12d |
|
99 |
98
|
rspcva |
|
100 |
81 99
|
sylan |
|
101 |
77 100
|
oveq12d |
|
102 |
|
inss1 |
|
103 |
|
ssfi |
|
104 |
78 102 103
|
sylancl |
|
105 |
|
hashcl |
|
106 |
104 105
|
syl |
|
107 |
106
|
nn0cnd |
|
108 |
|
hashcl |
|
109 |
81 108
|
syl |
|
110 |
109
|
nn0cnd |
|
111 |
|
inss1 |
|
112 |
|
ssfi |
|
113 |
78 111 112
|
sylancl |
|
114 |
|
hashcl |
|
115 |
113 114
|
syl |
|
116 |
115
|
nn0cnd |
|
117 |
|
hashun3 |
|
118 |
104 81 117
|
syl2anc |
|
119 |
|
indi |
|
120 |
119
|
fveq2i |
|
121 |
|
inindi |
|
122 |
121
|
fveq2i |
|
123 |
122
|
oveq2i |
|
124 |
118 120 123
|
3eqtr4g |
|
125 |
107 110 116 124
|
assraddsubd |
|
126 |
125
|
oveq2d |
|
127 |
|
hashcl |
|
128 |
127
|
adantl |
|
129 |
128
|
nn0cnd |
|
130 |
110 116
|
subcld |
|
131 |
129 107 130
|
subsub4d |
|
132 |
126 131
|
eqtr4d |
|
133 |
132
|
adantr |
|
134 |
|
disjdif |
|
135 |
134
|
a1i |
|
136 |
|
ssun1 |
|
137 |
136
|
sspwi |
|
138 |
|
undif |
|
139 |
137 138
|
mpbi |
|
140 |
139
|
eqcomi |
|
141 |
140
|
a1i |
|
142 |
|
simpll |
|
143 |
|
snfi |
|
144 |
|
unfi |
|
145 |
142 143 144
|
sylancl |
|
146 |
|
pwfi |
|
147 |
145 146
|
sylib |
|
148 |
54
|
a1i |
|
149 |
|
elpwi |
|
150 |
|
ssfi |
|
151 |
145 149 150
|
syl2an |
|
152 |
|
hashcl |
|
153 |
151 152
|
syl |
|
154 |
148 153
|
expcld |
|
155 |
|
simplr |
|
156 |
|
inss1 |
|
157 |
|
ssfi |
|
158 |
155 156 157
|
sylancl |
|
159 |
|
hashcl |
|
160 |
158 159
|
syl |
|
161 |
160
|
nn0cnd |
|
162 |
154 161
|
mulcld |
|
163 |
135 141 147 162
|
fsumsplit |
|
164 |
|
fveq2 |
|
165 |
164
|
oveq2d |
|
166 |
|
inteq |
|
167 |
|
vex |
|
168 |
167
|
intunsn |
|
169 |
166 168
|
eqtrdi |
|
170 |
169
|
ineq2d |
|
171 |
170
|
fveq2d |
|
172 |
165 171
|
oveq12d |
|
173 |
|
pwfi |
|
174 |
142 173
|
sylib |
|
175 |
|
eqid |
|
176 |
|
elpwi |
|
177 |
176
|
adantl |
|
178 |
|
unss1 |
|
179 |
177 178
|
syl |
|
180 |
|
vex |
|
181 |
|
vsnex |
|
182 |
180 181
|
unex |
|
183 |
182
|
elpw |
|
184 |
179 183
|
sylibr |
|
185 |
|
simpllr |
|
186 |
|
elpwi |
|
187 |
|
ssun2 |
|
188 |
167
|
snss |
|
189 |
187 188
|
mpbir |
|
190 |
189
|
a1i |
|
191 |
|
ssel |
|
192 |
186 190 191
|
syl2imc |
|
193 |
185 192
|
mtod |
|
194 |
184 193
|
eldifd |
|
195 |
|
eldifi |
|
196 |
195
|
adantl |
|
197 |
196
|
elpwid |
|
198 |
|
uncom |
|
199 |
197 198
|
sseqtrdi |
|
200 |
|
ssundif |
|
201 |
199 200
|
sylib |
|
202 |
|
vex |
|
203 |
202
|
elpw2 |
|
204 |
201 203
|
sylibr |
|
205 |
|
elpwunsn |
|
206 |
205
|
ad2antll |
|
207 |
206
|
snssd |
|
208 |
|
ssequn2 |
|
209 |
207 208
|
sylib |
|
210 |
209
|
eqcomd |
|
211 |
|
uneq1 |
|
212 |
|
undif1 |
|
213 |
211 212
|
eqtrdi |
|
214 |
213
|
eqeq2d |
|
215 |
210 214
|
syl5ibrcom |
|
216 |
176
|
ad2antrl |
|
217 |
|
simpllr |
|
218 |
216 217
|
ssneldd |
|
219 |
|
difsnb |
|
220 |
218 219
|
sylib |
|
221 |
220
|
eqcomd |
|
222 |
|
difeq1 |
|
223 |
|
difun2 |
|
224 |
222 223
|
eqtrdi |
|
225 |
224
|
eqeq2d |
|
226 |
221 225
|
syl5ibrcom |
|
227 |
215 226
|
impbid |
|
228 |
175 194 204 227
|
f1o2d |
|
229 |
|
uneq1 |
|
230 |
|
vex |
|
231 |
230 181
|
unex |
|
232 |
229 175 231
|
fvmpt |
|
233 |
232
|
adantl |
|
234 |
195 162
|
sylan2 |
|
235 |
172 174 228 233 234
|
fsumf1o |
|
236 |
|
uneq1 |
|
237 |
236
|
fveq2d |
|
238 |
237
|
oveq2d |
|
239 |
|
inteq |
|
240 |
239
|
ineq1d |
|
241 |
240
|
ineq2d |
|
242 |
241
|
fveq2d |
|
243 |
238 242
|
oveq12d |
|
244 |
243
|
cbvsumv |
|
245 |
54
|
a1i |
|
246 |
|
elpwi |
|
247 |
|
ssfi |
|
248 |
142 246 247
|
syl2an |
|
249 |
248 152
|
syl |
|
250 |
245 249
|
expp1d |
|
251 |
246
|
adantl |
|
252 |
|
simpllr |
|
253 |
251 252
|
ssneldd |
|
254 |
|
hashunsng |
|
255 |
254
|
elv |
|
256 |
248 253 255
|
syl2anc |
|
257 |
256
|
oveq2d |
|
258 |
137
|
sseli |
|
259 |
258 154
|
sylan2 |
|
260 |
245 259
|
mulcomd |
|
261 |
250 257 260
|
3eqtr4d |
|
262 |
259
|
mulm1d |
|
263 |
261 262
|
eqtrd |
|
264 |
263
|
oveq1d |
|
265 |
|
inss1 |
|
266 |
|
ssfi |
|
267 |
155 265 266
|
sylancl |
|
268 |
|
hashcl |
|
269 |
267 268
|
syl |
|
270 |
269
|
nn0cnd |
|
271 |
258 270
|
sylan2 |
|
272 |
259 271
|
mulneg1d |
|
273 |
264 272
|
eqtrd |
|
274 |
273
|
sumeq2dv |
|
275 |
244 274
|
eqtrid |
|
276 |
154 270
|
mulcld |
|
277 |
258 276
|
sylan2 |
|
278 |
174 277
|
fsumneg |
|
279 |
235 275 278
|
3eqtrd |
|
280 |
279
|
oveq2d |
|
281 |
137
|
a1i |
|
282 |
281
|
sselda |
|
283 |
282 162
|
syldan |
|
284 |
174 283
|
fsumcl |
|
285 |
282 276
|
syldan |
|
286 |
174 285
|
fsumcl |
|
287 |
284 286
|
negsubd |
|
288 |
163 280 287
|
3eqtrd |
|
289 |
288
|
adantr |
|
290 |
101 133 289
|
3eqtr4d |
|
291 |
290
|
ex |
|
292 |
291
|
ralrimdva |
|
293 |
|
ineq1 |
|
294 |
293
|
fveq2d |
|
295 |
66 294
|
oveq12d |
|
296 |
|
ineq1 |
|
297 |
296
|
fveq2d |
|
298 |
297
|
oveq2d |
|
299 |
298
|
sumeq2sdv |
|
300 |
295 299
|
eqeq12d |
|
301 |
300
|
cbvralvw |
|
302 |
292 301
|
syl6ibr |
|
303 |
16 24 37 45 65 302
|
findcard2s |
|
304 |
|
fveq2 |
|
305 |
|
ineq1 |
|
306 |
305
|
fveq2d |
|
307 |
304 306
|
oveq12d |
|
308 |
|
simpl |
|
309 |
308
|
ineq1d |
|
310 |
309
|
fveq2d |
|
311 |
310
|
oveq2d |
|
312 |
311
|
sumeq2dv |
|
313 |
307 312
|
eqeq12d |
|
314 |
313
|
rspccva |
|
315 |
303 314
|
sylan |
|