Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem12.1 |
|
2 |
|
fourierdlem12.2 |
|
3 |
|
fourierdlem12.3 |
|
4 |
|
fourierdlem12.4 |
|
5 |
1
|
fourierdlem2 |
|
6 |
2 5
|
syl |
|
7 |
3 6
|
mpbid |
|
8 |
7
|
simpld |
|
9 |
|
elmapi |
|
10 |
|
ffn |
|
11 |
|
fvelrnb |
|
12 |
8 9 10 11
|
4syl |
|
13 |
4 12
|
mpbid |
|
14 |
13
|
adantr |
|
15 |
8 9
|
syl |
|
16 |
15
|
adantr |
|
17 |
|
fzofzp1 |
|
18 |
17
|
adantl |
|
19 |
16 18
|
ffvelcdmd |
|
20 |
19
|
adantr |
|
21 |
20
|
3ad2antl1 |
|
22 |
|
frn |
|
23 |
15 22
|
syl |
|
24 |
23 4
|
sseldd |
|
25 |
24
|
ad2antrr |
|
26 |
25
|
3ad2antl1 |
|
27 |
16
|
ffvelcdmda |
|
28 |
27
|
3adant3 |
|
29 |
28
|
adantr |
|
30 |
|
simpr |
|
31 |
|
elfzoelz |
|
32 |
31
|
ad2antrr |
|
33 |
|
elfzelz |
|
34 |
33
|
ad2antlr |
|
35 |
|
zltp1le |
|
36 |
32 34 35
|
syl2anc |
|
37 |
30 36
|
mpbid |
|
38 |
32
|
peano2zd |
|
39 |
|
eluz |
|
40 |
38 34 39
|
syl2anc |
|
41 |
37 40
|
mpbird |
|
42 |
41
|
adantlll |
|
43 |
16
|
ad2antrr |
|
44 |
|
0zd |
|
45 |
|
elfzel2 |
|
46 |
45
|
ad2antlr |
|
47 |
|
elfzelz |
|
48 |
47
|
adantl |
|
49 |
|
0red |
|
50 |
47
|
zred |
|
51 |
50
|
adantl |
|
52 |
31
|
peano2zd |
|
53 |
52
|
zred |
|
54 |
53
|
adantr |
|
55 |
31
|
zred |
|
56 |
55
|
adantr |
|
57 |
|
elfzole1 |
|
58 |
57
|
adantr |
|
59 |
56
|
ltp1d |
|
60 |
49 56 54 58 59
|
lelttrd |
|
61 |
|
elfzle1 |
|
62 |
61
|
adantl |
|
63 |
49 54 51 60 62
|
ltletrd |
|
64 |
49 51 63
|
ltled |
|
65 |
64
|
adantlr |
|
66 |
50
|
adantl |
|
67 |
33
|
zred |
|
68 |
67
|
adantr |
|
69 |
45
|
zred |
|
70 |
69
|
adantr |
|
71 |
|
elfzle2 |
|
72 |
71
|
adantl |
|
73 |
|
elfzle2 |
|
74 |
73
|
adantr |
|
75 |
66 68 70 72 74
|
letrd |
|
76 |
75
|
adantll |
|
77 |
44 46 48 65 76
|
elfzd |
|
78 |
77
|
adantlll |
|
79 |
43 78
|
ffvelcdmd |
|
80 |
79
|
adantlr |
|
81 |
|
simp-4l |
|
82 |
|
0red |
|
83 |
|
elfzelz |
|
84 |
83
|
zred |
|
85 |
84
|
adantl |
|
86 |
|
0red |
|
87 |
53
|
adantr |
|
88 |
84
|
adantl |
|
89 |
|
0red |
|
90 |
55
|
ltp1d |
|
91 |
89 55 53 57 90
|
lelttrd |
|
92 |
91
|
adantr |
|
93 |
|
elfzle1 |
|
94 |
93
|
adantl |
|
95 |
86 87 88 92 94
|
ltletrd |
|
96 |
95
|
adantlr |
|
97 |
82 85 96
|
ltled |
|
98 |
97
|
adantlll |
|
99 |
98
|
adantlr |
|
100 |
84
|
adantl |
|
101 |
|
peano2rem |
|
102 |
67 101
|
syl |
|
103 |
102
|
adantr |
|
104 |
69
|
adantr |
|
105 |
|
elfzle2 |
|
106 |
105
|
adantl |
|
107 |
|
zlem1lt |
|
108 |
33 45 107
|
syl2anc |
|
109 |
73 108
|
mpbid |
|
110 |
109
|
adantr |
|
111 |
100 103 104 106 110
|
lelttrd |
|
112 |
111
|
adantlr |
|
113 |
112
|
adantlll |
|
114 |
83
|
adantl |
|
115 |
|
0zd |
|
116 |
45
|
ad3antlr |
|
117 |
|
elfzo |
|
118 |
114 115 116 117
|
syl3anc |
|
119 |
99 113 118
|
mpbir2and |
|
120 |
15
|
adantr |
|
121 |
|
elfzofz |
|
122 |
121
|
adantl |
|
123 |
120 122
|
ffvelcdmd |
|
124 |
|
fzofzp1 |
|
125 |
124
|
adantl |
|
126 |
120 125
|
ffvelcdmd |
|
127 |
|
eleq1w |
|
128 |
127
|
anbi2d |
|
129 |
|
fveq2 |
|
130 |
|
oveq1 |
|
131 |
130
|
fveq2d |
|
132 |
129 131
|
breq12d |
|
133 |
128 132
|
imbi12d |
|
134 |
7
|
simprrd |
|
135 |
134
|
r19.21bi |
|
136 |
133 135
|
chvarvv |
|
137 |
123 126 136
|
ltled |
|
138 |
81 119 137
|
syl2anc |
|
139 |
42 80 138
|
monoord |
|
140 |
139
|
3adantl3 |
|
141 |
15
|
ffvelcdmda |
|
142 |
141
|
3adant3 |
|
143 |
|
simp3 |
|
144 |
142 143
|
eqled |
|
145 |
144
|
3adant1r |
|
146 |
145
|
adantr |
|
147 |
21 29 26 140 146
|
letrd |
|
148 |
21 26 147
|
lensymd |
|
149 |
148
|
intnand |
|
150 |
67
|
ad2antlr |
|
151 |
55
|
ad3antlr |
|
152 |
|
simpr |
|
153 |
150 151 152
|
nltled |
|
154 |
153
|
3adantl3 |
|
155 |
|
eqcom |
|
156 |
155
|
biimpi |
|
157 |
156
|
adantr |
|
158 |
157
|
3ad2antl3 |
|
159 |
33
|
ad2antlr |
|
160 |
31
|
ad2antrr |
|
161 |
|
simpr |
|
162 |
|
eluz2 |
|
163 |
159 160 161 162
|
syl3anbrc |
|
164 |
163
|
adantlll |
|
165 |
16
|
ad2antrr |
|
166 |
|
0zd |
|
167 |
45
|
ad2antlr |
|
168 |
|
elfzelz |
|
169 |
168
|
adantl |
|
170 |
166 167 169
|
3jca |
|
171 |
|
0red |
|
172 |
67
|
adantr |
|
173 |
168
|
zred |
|
174 |
173
|
adantl |
|
175 |
|
elfzle1 |
|
176 |
175
|
adantr |
|
177 |
|
elfzle1 |
|
178 |
177
|
adantl |
|
179 |
171 172 174 176 178
|
letrd |
|
180 |
179
|
adantll |
|
181 |
173
|
adantl |
|
182 |
|
elfzoel2 |
|
183 |
182
|
zred |
|
184 |
183
|
adantr |
|
185 |
55
|
adantr |
|
186 |
|
elfzle2 |
|
187 |
186
|
adantl |
|
188 |
|
elfzolt2 |
|
189 |
188
|
adantr |
|
190 |
181 185 184 187 189
|
lelttrd |
|
191 |
181 184 190
|
ltled |
|
192 |
191
|
adantlr |
|
193 |
170 180 192
|
jca32 |
|
194 |
193
|
adantlll |
|
195 |
|
elfz2 |
|
196 |
194 195
|
sylibr |
|
197 |
165 196
|
ffvelcdmd |
|
198 |
197
|
adantlr |
|
199 |
|
simplll |
|
200 |
|
0red |
|
201 |
67
|
ad2antlr |
|
202 |
|
elfzelz |
|
203 |
202
|
zred |
|
204 |
203
|
adantl |
|
205 |
175
|
ad2antlr |
|
206 |
|
elfzle1 |
|
207 |
206
|
adantl |
|
208 |
200 201 204 205 207
|
letrd |
|
209 |
203
|
adantl |
|
210 |
55
|
adantr |
|
211 |
183
|
adantr |
|
212 |
|
peano2rem |
|
213 |
210 212
|
syl |
|
214 |
|
elfzle2 |
|
215 |
214
|
adantl |
|
216 |
210
|
ltm1d |
|
217 |
209 213 210 215 216
|
lelttrd |
|
218 |
188
|
adantr |
|
219 |
209 210 211 217 218
|
lttrd |
|
220 |
219
|
adantlr |
|
221 |
202
|
adantl |
|
222 |
|
0zd |
|
223 |
182
|
ad2antrr |
|
224 |
221 222 223 117
|
syl3anc |
|
225 |
208 220 224
|
mpbir2and |
|
226 |
225
|
adantlll |
|
227 |
199 226 137
|
syl2anc |
|
228 |
227
|
adantlr |
|
229 |
164 198 228
|
monoord |
|
230 |
229
|
3adantl3 |
|
231 |
158 230
|
eqbrtrd |
|
232 |
24
|
adantr |
|
233 |
|
elfzofz |
|
234 |
233
|
adantl |
|
235 |
16 234
|
ffvelcdmd |
|
236 |
232 235
|
lenltd |
|
237 |
236
|
adantr |
|
238 |
237
|
3ad2antl1 |
|
239 |
231 238
|
mpbid |
|
240 |
154 239
|
syldan |
|
241 |
240
|
intnanrd |
|
242 |
149 241
|
pm2.61dan |
|
243 |
242
|
intnand |
|
244 |
|
elioo3g |
|
245 |
243 244
|
sylnibr |
|
246 |
245
|
rexlimdv3a |
|
247 |
14 246
|
mpd |
|