Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem63.t |
|
2 |
|
fourierdlem63.p |
|
3 |
|
fourierdlem63.m |
|
4 |
|
fourierdlem63.q |
|
5 |
|
fourierdlem63.c |
|
6 |
|
fourierdlem63.d |
|
7 |
|
fourierdlem63.cltd |
|
8 |
|
fourierdlem63.o |
|
9 |
|
fourierdlem63.h |
|
10 |
|
fourierdlem63.n |
|
11 |
|
fourierdlem63.s |
|
12 |
|
fourierdlem63.e |
|
13 |
|
fourierdlem63.k |
|
14 |
|
fourierdlem63.j |
|
15 |
|
fourierdlem63.y |
|
16 |
|
fourierdlem63.eyltqk |
|
17 |
|
fourierdlem63.x |
|
18 |
12
|
a1i |
|
19 |
|
id |
|
20 |
|
oveq2 |
|
21 |
20
|
oveq1d |
|
22 |
21
|
fveq2d |
|
23 |
22
|
oveq1d |
|
24 |
19 23
|
oveq12d |
|
25 |
24
|
adantl |
|
26 |
1 2 3 4 5 6 7 8 9 10 11
|
fourierdlem54 |
|
27 |
26
|
simpld |
|
28 |
27
|
simprd |
|
29 |
27
|
simpld |
|
30 |
8
|
fourierdlem2 |
|
31 |
29 30
|
syl |
|
32 |
28 31
|
mpbid |
|
33 |
32
|
simpld |
|
34 |
|
elmapi |
|
35 |
33 34
|
syl |
|
36 |
|
fzofzp1 |
|
37 |
14 36
|
syl |
|
38 |
35 37
|
ffvelrnd |
|
39 |
2 3 4
|
fourierdlem11 |
|
40 |
39
|
simp2d |
|
41 |
40 38
|
resubcld |
|
42 |
39
|
simp1d |
|
43 |
40 42
|
resubcld |
|
44 |
1 43
|
eqeltrid |
|
45 |
39
|
simp3d |
|
46 |
42 40
|
posdifd |
|
47 |
45 46
|
mpbid |
|
48 |
47 1
|
breqtrrdi |
|
49 |
48
|
gt0ne0d |
|
50 |
41 44 49
|
redivcld |
|
51 |
50
|
flcld |
|
52 |
51
|
zred |
|
53 |
52 44
|
remulcld |
|
54 |
38 53
|
readdcld |
|
55 |
18 25 38 54
|
fvmptd |
|
56 |
55 54
|
eqeltrd |
|
57 |
2
|
fourierdlem2 |
|
58 |
3 57
|
syl |
|
59 |
4 58
|
mpbid |
|
60 |
59
|
simpld |
|
61 |
|
elmapi |
|
62 |
60 61
|
syl |
|
63 |
62 13
|
ffvelrnd |
|
64 |
5
|
adantr |
|
65 |
6
|
adantr |
|
66 |
42
|
rexrd |
|
67 |
|
iocssre |
|
68 |
66 40 67
|
syl2anc |
|
69 |
42 40 45 1 12
|
fourierdlem4 |
|
70 |
|
elfzofz |
|
71 |
14 70
|
syl |
|
72 |
35 71
|
ffvelrnd |
|
73 |
38
|
rexrd |
|
74 |
|
elico2 |
|
75 |
72 73 74
|
syl2anc |
|
76 |
15 75
|
mpbid |
|
77 |
76
|
simp1d |
|
78 |
69 77
|
ffvelrnd |
|
79 |
68 78
|
sseldd |
|
80 |
79 77
|
resubcld |
|
81 |
63 80
|
resubcld |
|
82 |
81
|
adantr |
|
83 |
|
icossicc |
|
84 |
5
|
rexrd |
|
85 |
6
|
rexrd |
|
86 |
8 29 28
|
fourierdlem15 |
|
87 |
84 85 86 14
|
fourierdlem8 |
|
88 |
83 87
|
sstrid |
|
89 |
88 15
|
sseldd |
|
90 |
|
elicc2 |
|
91 |
5 6 90
|
syl2anc |
|
92 |
89 91
|
mpbid |
|
93 |
92
|
simp2d |
|
94 |
63 79
|
resubcld |
|
95 |
79 63
|
posdifd |
|
96 |
16 95
|
mpbid |
|
97 |
94 96
|
elrpd |
|
98 |
77 97
|
ltaddrpd |
|
99 |
63
|
recnd |
|
100 |
79
|
recnd |
|
101 |
77
|
recnd |
|
102 |
99 100 101
|
subsub3d |
|
103 |
99 101
|
addcomd |
|
104 |
103
|
oveq1d |
|
105 |
101 99 100
|
addsubassd |
|
106 |
102 104 105
|
3eqtrrd |
|
107 |
98 106
|
breqtrd |
|
108 |
5 77 81 93 107
|
lelttrd |
|
109 |
5 81 108
|
ltled |
|
110 |
109
|
adantr |
|
111 |
38
|
adantr |
|
112 |
63
|
adantr |
|
113 |
56 38
|
resubcld |
|
114 |
113
|
adantr |
|
115 |
112 114
|
resubcld |
|
116 |
76
|
simp3d |
|
117 |
77 38 116
|
ltled |
|
118 |
42 40 45 1 12 77 38 117
|
fourierdlem7 |
|
119 |
113 80 63 118
|
lesub2dd |
|
120 |
119
|
adantr |
|
121 |
99
|
adantr |
|
122 |
56
|
recnd |
|
123 |
122
|
adantr |
|
124 |
111
|
recnd |
|
125 |
121 123 124
|
subsubd |
|
126 |
99 122
|
subcld |
|
127 |
38
|
recnd |
|
128 |
126 127
|
addcomd |
|
129 |
128
|
adantr |
|
130 |
125 129
|
eqtrd |
|
131 |
|
simpr |
|
132 |
56
|
adantr |
|
133 |
112 132
|
sublt0d |
|
134 |
131 133
|
mpbird |
|
135 |
112 132
|
resubcld |
|
136 |
|
ltaddneg |
|
137 |
135 111 136
|
syl2anc |
|
138 |
134 137
|
mpbid |
|
139 |
130 138
|
eqbrtrd |
|
140 |
82 115 111 120 139
|
lelttrd |
|
141 |
86 37
|
ffvelrnd |
|
142 |
|
elicc2 |
|
143 |
5 6 142
|
syl2anc |
|
144 |
141 143
|
mpbid |
|
145 |
144
|
simp3d |
|
146 |
145
|
adantr |
|
147 |
82 111 65 140 146
|
ltletrd |
|
148 |
82 65 147
|
ltled |
|
149 |
64 65 82 110 148
|
eliccd |
|
150 |
|
id |
|
151 |
|
oveq2 |
|
152 |
151
|
oveq1d |
|
153 |
152
|
fveq2d |
|
154 |
153
|
oveq1d |
|
155 |
150 154
|
oveq12d |
|
156 |
155
|
adantl |
|
157 |
40 77
|
resubcld |
|
158 |
157 44 49
|
redivcld |
|
159 |
158
|
flcld |
|
160 |
159
|
zred |
|
161 |
160 44
|
remulcld |
|
162 |
77 161
|
readdcld |
|
163 |
18 156 77 162
|
fvmptd |
|
164 |
163
|
oveq1d |
|
165 |
164
|
oveq1d |
|
166 |
161
|
recnd |
|
167 |
101 166
|
pncan2d |
|
168 |
167
|
oveq1d |
|
169 |
160
|
recnd |
|
170 |
44
|
recnd |
|
171 |
169 170 49
|
divcan4d |
|
172 |
165 168 171
|
3eqtrd |
|
173 |
172 159
|
eqeltrd |
|
174 |
80
|
recnd |
|
175 |
174 170 49
|
divcan1d |
|
176 |
175
|
oveq2d |
|
177 |
99 174
|
npcand |
|
178 |
176 177
|
eqtrd |
|
179 |
|
ffun |
|
180 |
62 179
|
syl |
|
181 |
62
|
fdmd |
|
182 |
13 181
|
eleqtrrd |
|
183 |
|
fvelrn |
|
184 |
180 182 183
|
syl2anc |
|
185 |
178 184
|
eqeltrd |
|
186 |
|
oveq1 |
|
187 |
186
|
oveq2d |
|
188 |
187
|
eleq1d |
|
189 |
188
|
rspcev |
|
190 |
173 185 189
|
syl2anc |
|
191 |
190
|
adantr |
|
192 |
|
oveq1 |
|
193 |
192
|
eleq1d |
|
194 |
193
|
rexbidv |
|
195 |
194
|
elrab |
|
196 |
149 191 195
|
sylanbrc |
|
197 |
|
elun2 |
|
198 |
196 197
|
syl |
|
199 |
198 17 9
|
3eltr4g |
|
200 |
|
elfzelz |
|
201 |
200
|
ad2antlr |
|
202 |
|
elfzoelz |
|
203 |
14 202
|
syl |
|
204 |
203
|
ad2antrr |
|
205 |
|
simpr |
|
206 |
26
|
simprd |
|
207 |
206
|
ad2antrr |
|
208 |
71
|
ad2antrr |
|
209 |
|
simplr |
|
210 |
|
isorel |
|
211 |
207 208 209 210
|
syl12anc |
|
212 |
205 211
|
mpbird |
|
213 |
212
|
adantrr |
|
214 |
|
simpr |
|
215 |
206
|
ad2antrr |
|
216 |
|
simplr |
|
217 |
37
|
ad2antrr |
|
218 |
|
isorel |
|
219 |
215 216 217 218
|
syl12anc |
|
220 |
214 219
|
mpbird |
|
221 |
220
|
adantrl |
|
222 |
|
btwnnz |
|
223 |
204 213 221 222
|
syl3anc |
|
224 |
201 223
|
pm2.65da |
|
225 |
224
|
adantlr |
|
226 |
72
|
ad2antrr |
|
227 |
77
|
ad2antrr |
|
228 |
35
|
ffvelrnda |
|
229 |
228
|
adantr |
|
230 |
76
|
simp2d |
|
231 |
230
|
ad2antrr |
|
232 |
107 17
|
breqtrrdi |
|
233 |
232
|
adantr |
|
234 |
|
eqcom |
|
235 |
234
|
biimpri |
|
236 |
235
|
adantl |
|
237 |
233 236
|
breqtrd |
|
238 |
237
|
adantlr |
|
239 |
226 227 229 231 238
|
lelttrd |
|
240 |
239
|
adantllr |
|
241 |
|
simpr |
|
242 |
17 140
|
eqbrtrid |
|
243 |
242
|
adantr |
|
244 |
241 243
|
eqbrtrd |
|
245 |
244
|
adantlr |
|
246 |
240 245
|
jca |
|
247 |
225 246
|
mtand |
|
248 |
247
|
nrexdv |
|
249 |
|
isof1o |
|
250 |
206 249
|
syl |
|
251 |
|
f1ofo |
|
252 |
250 251
|
syl |
|
253 |
|
foelrn |
|
254 |
252 253
|
sylan |
|
255 |
234
|
rexbii |
|
256 |
254 255
|
sylib |
|
257 |
256
|
adantlr |
|
258 |
248 257
|
mtand |
|
259 |
199 258
|
pm2.65da |
|
260 |
56 63 259
|
nltled |
|