Step |
Hyp |
Ref |
Expression |
1 |
|
ibladdnc.1 |
|
2 |
|
ibladdnc.2 |
|
3 |
|
ibladdnc.3 |
|
4 |
|
ibladdnc.4 |
|
5 |
|
ibladdnc.m |
|
6 |
|
itgaddnclem.1 |
|
7 |
|
itgaddnclem.2 |
|
8 |
|
max0sub |
|
9 |
6 8
|
syl |
|
10 |
|
max0sub |
|
11 |
7 10
|
syl |
|
12 |
9 11
|
oveq12d |
|
13 |
|
0re |
|
14 |
|
ifcl |
|
15 |
6 13 14
|
sylancl |
|
16 |
15
|
recnd |
|
17 |
|
ifcl |
|
18 |
7 13 17
|
sylancl |
|
19 |
18
|
recnd |
|
20 |
6
|
renegcld |
|
21 |
|
ifcl |
|
22 |
20 13 21
|
sylancl |
|
23 |
22
|
recnd |
|
24 |
7
|
renegcld |
|
25 |
|
ifcl |
|
26 |
24 13 25
|
sylancl |
|
27 |
26
|
recnd |
|
28 |
16 19 23 27
|
addsub4d |
|
29 |
6 7
|
readdcld |
|
30 |
|
max0sub |
|
31 |
29 30
|
syl |
|
32 |
12 28 31
|
3eqtr4rd |
|
33 |
29
|
renegcld |
|
34 |
|
ifcl |
|
35 |
33 13 34
|
sylancl |
|
36 |
35
|
recnd |
|
37 |
15 18
|
readdcld |
|
38 |
37
|
recnd |
|
39 |
|
ifcl |
|
40 |
29 13 39
|
sylancl |
|
41 |
40
|
recnd |
|
42 |
22 26
|
readdcld |
|
43 |
42
|
recnd |
|
44 |
36 38 41 43
|
addsubeq4d |
|
45 |
32 44
|
mpbird |
|
46 |
45
|
itgeq2dv |
|
47 |
6 2 7 4 5
|
ibladdnc |
|
48 |
29
|
iblre |
|
49 |
47 48
|
mpbid |
|
50 |
49
|
simprd |
|
51 |
6
|
iblre |
|
52 |
2 51
|
mpbid |
|
53 |
52
|
simpld |
|
54 |
7
|
iblre |
|
55 |
4 54
|
mpbid |
|
56 |
55
|
simpld |
|
57 |
|
iblmbf |
|
58 |
2 57
|
syl |
|
59 |
|
iblmbf |
|
60 |
4 59
|
syl |
|
61 |
58 6 60 7 5
|
mbfposadd |
|
62 |
15 53 18 56 61
|
ibladdnc |
|
63 |
|
max1 |
|
64 |
13 6 63
|
sylancr |
|
65 |
|
max1 |
|
66 |
13 7 65
|
sylancr |
|
67 |
15 18 64 66
|
addge0d |
|
68 |
67
|
iftrued |
|
69 |
68
|
oveq2d |
|
70 |
69
|
mpteq2dva |
|
71 |
29 5
|
mbfneg |
|
72 |
6
|
recnd |
|
73 |
7
|
recnd |
|
74 |
72 73
|
negdid |
|
75 |
74
|
oveq1d |
|
76 |
20
|
recnd |
|
77 |
24
|
recnd |
|
78 |
76 77 16 19
|
add4d |
|
79 |
|
negeq |
|
80 |
|
neg0 |
|
81 |
79 80
|
eqtrdi |
|
82 |
|
0le0 |
|
83 |
82 81
|
breqtrrid |
|
84 |
83
|
iftrued |
|
85 |
|
id |
|
86 |
82 85
|
breqtrrid |
|
87 |
86
|
iftrued |
|
88 |
87 85
|
eqtrd |
|
89 |
81 88
|
oveq12d |
|
90 |
|
00id |
|
91 |
89 90
|
eqtrdi |
|
92 |
81 84 91
|
3eqtr4rd |
|
93 |
92
|
adantl |
|
94 |
|
ovif2 |
|
95 |
72
|
negne0bd |
|
96 |
95
|
biimpa |
|
97 |
6
|
le0neg2d |
|
98 |
|
leloe |
|
99 |
20 13 98
|
sylancl |
|
100 |
97 99
|
bitrd |
|
101 |
|
df-ne |
|
102 |
|
biorf |
|
103 |
101 102
|
sylbi |
|
104 |
|
orcom |
|
105 |
103 104
|
bitr2di |
|
106 |
100 105
|
sylan9bb |
|
107 |
96 106
|
syldan |
|
108 |
|
ltnle |
|
109 |
20 13 108
|
sylancl |
|
110 |
109
|
adantr |
|
111 |
107 110
|
bitrd |
|
112 |
76 72
|
addcomd |
|
113 |
72
|
negidd |
|
114 |
112 113
|
eqtrd |
|
115 |
114
|
adantr |
|
116 |
76
|
addid1d |
|
117 |
116
|
adantr |
|
118 |
111 115 117
|
ifbieq12d |
|
119 |
|
ifnot |
|
120 |
118 119
|
eqtrdi |
|
121 |
94 120
|
syl5eq |
|
122 |
93 121
|
pm2.61dane |
|
123 |
|
negeq |
|
124 |
123 80
|
eqtrdi |
|
125 |
82 124
|
breqtrrid |
|
126 |
125
|
iftrued |
|
127 |
|
id |
|
128 |
82 127
|
breqtrrid |
|
129 |
128
|
iftrued |
|
130 |
129 127
|
eqtrd |
|
131 |
124 130
|
oveq12d |
|
132 |
131 90
|
eqtrdi |
|
133 |
124 126 132
|
3eqtr4rd |
|
134 |
133
|
adantl |
|
135 |
|
ovif2 |
|
136 |
73
|
negne0bd |
|
137 |
136
|
biimpa |
|
138 |
7
|
le0neg2d |
|
139 |
|
leloe |
|
140 |
24 13 139
|
sylancl |
|
141 |
138 140
|
bitrd |
|
142 |
|
df-ne |
|
143 |
|
biorf |
|
144 |
142 143
|
sylbi |
|
145 |
|
orcom |
|
146 |
144 145
|
bitr2di |
|
147 |
141 146
|
sylan9bb |
|
148 |
137 147
|
syldan |
|
149 |
|
ltnle |
|
150 |
24 13 149
|
sylancl |
|
151 |
150
|
adantr |
|
152 |
148 151
|
bitrd |
|
153 |
77 73
|
addcomd |
|
154 |
73
|
negidd |
|
155 |
153 154
|
eqtrd |
|
156 |
155
|
adantr |
|
157 |
77
|
addid1d |
|
158 |
157
|
adantr |
|
159 |
152 156 158
|
ifbieq12d |
|
160 |
|
ifnot |
|
161 |
159 160
|
eqtrdi |
|
162 |
135 161
|
syl5eq |
|
163 |
134 162
|
pm2.61dane |
|
164 |
122 163
|
oveq12d |
|
165 |
75 78 164
|
3eqtrd |
|
166 |
165
|
mpteq2dva |
|
167 |
6 58
|
mbfneg |
|
168 |
7 60
|
mbfneg |
|
169 |
74
|
mpteq2dva |
|
170 |
169 71
|
eqeltrrd |
|
171 |
167 20 168 24 170
|
mbfposadd |
|
172 |
166 171
|
eqeltrd |
|
173 |
71 33 61 37 172
|
mbfposadd |
|
174 |
70 173
|
eqeltrrd |
|
175 |
|
max1 |
|
176 |
13 33 175
|
sylancr |
|
177 |
35 50 37 62 174 35 37 176 67
|
itgaddnclem1 |
|
178 |
49
|
simpld |
|
179 |
52
|
simprd |
|
180 |
55
|
simprd |
|
181 |
22 179 26 180 171
|
ibladdnc |
|
182 |
|
max1 |
|
183 |
13 20 182
|
sylancr |
|
184 |
|
max1 |
|
185 |
13 24 184
|
sylancr |
|
186 |
22 26 183 185
|
addge0d |
|
187 |
186
|
iftrued |
|
188 |
187
|
oveq2d |
|
189 |
188
|
mpteq2dva |
|
190 |
72 73 23 27
|
add4d |
|
191 |
84 81
|
eqtrd |
|
192 |
85 191
|
oveq12d |
|
193 |
192 90
|
eqtrdi |
|
194 |
85 87 193
|
3eqtr4rd |
|
195 |
194
|
adantl |
|
196 |
|
ovif2 |
|
197 |
6
|
le0neg1d |
|
198 |
|
leloe |
|
199 |
6 13 198
|
sylancl |
|
200 |
197 199
|
bitr3d |
|
201 |
|
df-ne |
|
202 |
|
biorf |
|
203 |
201 202
|
sylbi |
|
204 |
|
orcom |
|
205 |
203 204
|
bitr2di |
|
206 |
200 205
|
sylan9bb |
|
207 |
|
ltnle |
|
208 |
6 13 207
|
sylancl |
|
209 |
208
|
adantr |
|
210 |
206 209
|
bitrd |
|
211 |
113
|
adantr |
|
212 |
72
|
addid1d |
|
213 |
212
|
adantr |
|
214 |
210 211 213
|
ifbieq12d |
|
215 |
|
ifnot |
|
216 |
214 215
|
eqtrdi |
|
217 |
196 216
|
syl5eq |
|
218 |
195 217
|
pm2.61dane |
|
219 |
126 124
|
eqtrd |
|
220 |
127 219
|
oveq12d |
|
221 |
220 90
|
eqtrdi |
|
222 |
127 129 221
|
3eqtr4rd |
|
223 |
222
|
adantl |
|
224 |
|
ovif2 |
|
225 |
7
|
le0neg1d |
|
226 |
|
leloe |
|
227 |
7 13 226
|
sylancl |
|
228 |
225 227
|
bitr3d |
|
229 |
|
df-ne |
|
230 |
|
biorf |
|
231 |
229 230
|
sylbi |
|
232 |
|
orcom |
|
233 |
231 232
|
bitr2di |
|
234 |
228 233
|
sylan9bb |
|
235 |
|
ltnle |
|
236 |
7 13 235
|
sylancl |
|
237 |
236
|
adantr |
|
238 |
234 237
|
bitrd |
|
239 |
154
|
adantr |
|
240 |
73
|
addid1d |
|
241 |
240
|
adantr |
|
242 |
238 239 241
|
ifbieq12d |
|
243 |
|
ifnot |
|
244 |
242 243
|
eqtrdi |
|
245 |
224 244
|
syl5eq |
|
246 |
223 245
|
pm2.61dane |
|
247 |
218 246
|
oveq12d |
|
248 |
190 247
|
eqtrd |
|
249 |
248
|
mpteq2dva |
|
250 |
249 61
|
eqeltrd |
|
251 |
5 29 171 42 250
|
mbfposadd |
|
252 |
189 251
|
eqeltrrd |
|
253 |
|
max1 |
|
254 |
13 29 253
|
sylancr |
|
255 |
40 178 42 181 252 40 42 254 186
|
itgaddnclem1 |
|
256 |
46 177 255
|
3eqtr3d |
|
257 |
35 50
|
itgcl |
|
258 |
15 53 18 56 61 15 18 64 66
|
itgaddnclem1 |
|
259 |
15 53
|
itgcl |
|
260 |
18 56
|
itgcl |
|
261 |
259 260
|
addcld |
|
262 |
258 261
|
eqeltrd |
|
263 |
40 178
|
itgcl |
|
264 |
22 179 26 180 171 22 26 183 185
|
itgaddnclem1 |
|
265 |
22 179
|
itgcl |
|
266 |
26 180
|
itgcl |
|
267 |
265 266
|
addcld |
|
268 |
264 267
|
eqeltrd |
|
269 |
257 262 263 268
|
addsubeq4d |
|
270 |
256 269
|
mpbid |
|
271 |
258 264
|
oveq12d |
|
272 |
259 260 265 266
|
addsub4d |
|
273 |
270 271 272
|
3eqtrd |
|
274 |
29 47
|
itgreval |
|
275 |
6 2
|
itgreval |
|
276 |
7 4
|
itgreval |
|
277 |
275 276
|
oveq12d |
|
278 |
273 274 277
|
3eqtr4d |
|