Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem68.f |
|
2 |
|
fourierdlem68.xre |
|
3 |
|
fourierdlem68.a |
|
4 |
|
fourierdlem68.b |
|
5 |
|
fourierdlem68.altb |
|
6 |
|
fourierdlem68.ab |
|
7 |
|
fourierdlem68.n0 |
|
8 |
|
fourierdlem68.fdv |
|
9 |
|
fourierdlem68.d |
|
10 |
|
fourierdlem68.fbd |
|
11 |
|
fourierdlem68.e |
|
12 |
|
fourierdlem68.fdvbd |
|
13 |
|
fourierdlem68.c |
|
14 |
|
fourierdlem68.o |
|
15 |
|
ioossicc |
|
16 |
15 6
|
sstrid |
|
17 |
15
|
sseli |
|
18 |
7 17
|
nsyl |
|
19 |
1 2 3 4 8 16 18 13 14
|
fourierdlem57 |
|
20 |
19
|
simpli |
|
21 |
20
|
simpld |
|
22 |
21
|
fdmd |
|
23 |
|
eqid |
|
24 |
3 4 5
|
ltled |
|
25 |
|
2re |
|
26 |
25
|
a1i |
|
27 |
3 4
|
iccssred |
|
28 |
27
|
sselda |
|
29 |
28
|
rehalfcld |
|
30 |
29
|
resincld |
|
31 |
26 30
|
remulcld |
|
32 |
|
2cnd |
|
33 |
30
|
recnd |
|
34 |
|
2ne0 |
|
35 |
34
|
a1i |
|
36 |
6
|
sselda |
|
37 |
|
eqcom |
|
38 |
37
|
biimpi |
|
39 |
38
|
adantl |
|
40 |
|
simpl |
|
41 |
39 40
|
eqeltrd |
|
42 |
41
|
adantll |
|
43 |
7
|
ad2antrr |
|
44 |
42 43
|
pm2.65da |
|
45 |
44
|
neqned |
|
46 |
|
fourierdlem44 |
|
47 |
36 45 46
|
syl2anc |
|
48 |
32 33 35 47
|
mulne0d |
|
49 |
|
eldifsn |
|
50 |
31 48 49
|
sylanbrc |
|
51 |
50 23
|
fmptd |
|
52 |
|
difss |
|
53 |
|
ax-resscn |
|
54 |
52 53
|
sstri |
|
55 |
54
|
a1i |
|
56 |
27 53
|
sstrdi |
|
57 |
|
2cnd |
|
58 |
|
ssid |
|
59 |
58
|
a1i |
|
60 |
56 57 59
|
constcncfg |
|
61 |
|
sincn |
|
62 |
61
|
a1i |
|
63 |
56 59
|
idcncfg |
|
64 |
|
eldifsn |
|
65 |
32 35 64
|
sylanbrc |
|
66 |
|
eqid |
|
67 |
65 66
|
fmptd |
|
68 |
|
difssd |
|
69 |
|
cncffvrn |
|
70 |
68 60 69
|
syl2anc |
|
71 |
67 70
|
mpbird |
|
72 |
63 71
|
divcncf |
|
73 |
62 72
|
cncfmpt1f |
|
74 |
60 73
|
mulcncf |
|
75 |
|
cncffvrn |
|
76 |
55 74 75
|
syl2anc |
|
77 |
51 76
|
mpbird |
|
78 |
23 3 4 24 77
|
cncficcgt0 |
|
79 |
|
reelprrecn |
|
80 |
79
|
a1i |
|
81 |
1
|
adantr |
|
82 |
2
|
adantr |
|
83 |
|
elioore |
|
84 |
83
|
adantl |
|
85 |
82 84
|
readdcld |
|
86 |
81 85
|
ffvelrnd |
|
87 |
13
|
adantr |
|
88 |
86 87
|
resubcld |
|
89 |
88
|
recnd |
|
90 |
89
|
3ad2antl1 |
|
91 |
79
|
a1i |
|
92 |
86
|
recnd |
|
93 |
8
|
adantr |
|
94 |
2 3
|
readdcld |
|
95 |
94
|
rexrd |
|
96 |
95
|
adantr |
|
97 |
2 4
|
readdcld |
|
98 |
97
|
rexrd |
|
99 |
98
|
adantr |
|
100 |
3
|
adantr |
|
101 |
100
|
rexrd |
|
102 |
4
|
rexrd |
|
103 |
102
|
adantr |
|
104 |
|
simpr |
|
105 |
|
ioogtlb |
|
106 |
101 103 104 105
|
syl3anc |
|
107 |
100 84 82 106
|
ltadd2dd |
|
108 |
4
|
adantr |
|
109 |
|
iooltub |
|
110 |
101 103 104 109
|
syl3anc |
|
111 |
84 108 82 110
|
ltadd2dd |
|
112 |
96 99 85 107 111
|
eliood |
|
113 |
93 112
|
ffvelrnd |
|
114 |
|
eqid |
|
115 |
1 2 3 4 114 8
|
fourierdlem28 |
|
116 |
87
|
recnd |
|
117 |
|
0red |
|
118 |
|
iooretop |
|
119 |
|
eqid |
|
120 |
119
|
tgioo2 |
|
121 |
118 120
|
eleqtri |
|
122 |
121
|
a1i |
|
123 |
13
|
recnd |
|
124 |
91 122 123
|
dvmptconst |
|
125 |
91 92 113 115 116 117 124
|
dvmptsub |
|
126 |
113
|
recnd |
|
127 |
126
|
subid1d |
|
128 |
127
|
mpteq2dva |
|
129 |
125 128
|
eqtrd |
|
130 |
129
|
3ad2ant1 |
|
131 |
126
|
3ad2antl1 |
|
132 |
|
2cnd |
|
133 |
83
|
recnd |
|
134 |
133
|
halfcld |
|
135 |
134
|
sincld |
|
136 |
132 135
|
mulcld |
|
137 |
136
|
adantl |
|
138 |
11
|
3ad2ant1 |
|
139 |
|
1re |
|
140 |
25 139
|
remulcli |
|
141 |
140
|
a1i |
|
142 |
|
1red |
|
143 |
123
|
abscld |
|
144 |
9 143
|
readdcld |
|
145 |
144
|
3ad2ant1 |
|
146 |
|
simpl |
|
147 |
146 112
|
jca |
|
148 |
|
eleq1 |
|
149 |
148
|
anbi2d |
|
150 |
|
fveq2 |
|
151 |
150
|
fveq2d |
|
152 |
151
|
breq1d |
|
153 |
149 152
|
imbi12d |
|
154 |
153 12
|
vtoclg |
|
155 |
85 147 154
|
sylc |
|
156 |
155
|
3ad2antl1 |
|
157 |
132 135
|
absmuld |
|
158 |
|
0le2 |
|
159 |
|
absid |
|
160 |
25 158 159
|
mp2an |
|
161 |
160
|
oveq1i |
|
162 |
135
|
abscld |
|
163 |
|
1red |
|
164 |
25
|
a1i |
|
165 |
158
|
a1i |
|
166 |
83
|
rehalfcld |
|
167 |
|
abssinbd |
|
168 |
166 167
|
syl |
|
169 |
162 163 164 165 168
|
lemul2ad |
|
170 |
161 169
|
eqbrtrid |
|
171 |
157 170
|
eqbrtrd |
|
172 |
171
|
adantl |
|
173 |
|
abscosbd |
|
174 |
104 166 173
|
3syl |
|
175 |
174
|
3ad2antl1 |
|
176 |
89
|
abscld |
|
177 |
92
|
abscld |
|
178 |
116
|
abscld |
|
179 |
177 178
|
readdcld |
|
180 |
9
|
adantr |
|
181 |
180 178
|
readdcld |
|
182 |
92 116
|
abs2dif2d |
|
183 |
|
fveq2 |
|
184 |
183
|
fveq2d |
|
185 |
184
|
breq1d |
|
186 |
149 185
|
imbi12d |
|
187 |
186 10
|
vtoclg |
|
188 |
112 147 187
|
sylc |
|
189 |
177 180 178 188
|
leadd1dd |
|
190 |
176 179 181 182 189
|
letrd |
|
191 |
190
|
3ad2antl1 |
|
192 |
19
|
simpri |
|
193 |
192
|
a1i |
|
194 |
134
|
coscld |
|
195 |
194
|
adantl |
|
196 |
|
simp2 |
|
197 |
|
oveq1 |
|
198 |
197
|
fveq2d |
|
199 |
198
|
oveq2d |
|
200 |
199
|
fveq2d |
|
201 |
200
|
breq2d |
|
202 |
201
|
cbvralvw |
|
203 |
|
nfv |
|
204 |
|
nfra1 |
|
205 |
203 204
|
nfan |
|
206 |
|
simplr |
|
207 |
15 104
|
sseldi |
|
208 |
207
|
adantlr |
|
209 |
|
rspa |
|
210 |
206 208 209
|
syl2anc |
|
211 |
210
|
ex |
|
212 |
205 211
|
ralrimi |
|
213 |
202 212
|
sylan2b |
|
214 |
213
|
3adant2 |
|
215 |
|
eqid |
|
216 |
80 90 130 131 137 138 141 142 145 156 172 175 191 193 195 196 214 215
|
dvdivbd |
|
217 |
216
|
rexlimdv3a |
|
218 |
78 217
|
mpd |
|
219 |
|
nfcv |
|
220 |
|
nfcv |
|
221 |
|
nfmpt1 |
|
222 |
14 221
|
nfcxfr |
|
223 |
219 220 222
|
nfov |
|
224 |
223
|
nfdm |
|
225 |
|
nfcv |
|
226 |
224 225
|
raleqf |
|
227 |
22 226
|
syl |
|
228 |
227
|
rexbidv |
|
229 |
218 228
|
mpbird |
|
230 |
14
|
a1i |
|
231 |
230
|
oveq2d |
|
232 |
231
|
fveq1d |
|
233 |
232
|
fveq2d |
|
234 |
233
|
breq1d |
|
235 |
234
|
rexralbidv |
|
236 |
229 235
|
mpbird |
|
237 |
22 236
|
jca |
|