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 |
8 9 10
|
3syl |
|
12 |
|
fvelrnb |
|
13 |
11 12
|
syl |
|
14 |
4 13
|
mpbid |
|
15 |
14
|
adantr |
|
16 |
8 9
|
syl |
|
17 |
16
|
adantr |
|
18 |
|
fzofzp1 |
|
19 |
18
|
adantl |
|
20 |
17 19
|
ffvelrnd |
|
21 |
20
|
adantr |
|
22 |
21
|
3ad2antl1 |
|
23 |
|
frn |
|
24 |
16 23
|
syl |
|
25 |
24 4
|
sseldd |
|
26 |
25
|
ad2antrr |
|
27 |
26
|
3ad2antl1 |
|
28 |
17
|
ffvelrnda |
|
29 |
28
|
3adant3 |
|
30 |
29
|
adantr |
|
31 |
|
simpr |
|
32 |
|
elfzoelz |
|
33 |
32
|
ad2antrr |
|
34 |
|
elfzelz |
|
35 |
34
|
ad2antlr |
|
36 |
|
zltp1le |
|
37 |
33 35 36
|
syl2anc |
|
38 |
31 37
|
mpbid |
|
39 |
33
|
peano2zd |
|
40 |
|
eluz |
|
41 |
39 35 40
|
syl2anc |
|
42 |
38 41
|
mpbird |
|
43 |
42
|
adantlll |
|
44 |
17
|
ad2antrr |
|
45 |
|
0red |
|
46 |
|
elfzelz |
|
47 |
46
|
zred |
|
48 |
47
|
adantl |
|
49 |
32
|
peano2zd |
|
50 |
49
|
zred |
|
51 |
50
|
adantr |
|
52 |
32
|
zred |
|
53 |
52
|
adantr |
|
54 |
|
elfzole1 |
|
55 |
54
|
adantr |
|
56 |
53
|
ltp1d |
|
57 |
45 53 51 55 56
|
lelttrd |
|
58 |
|
elfzle1 |
|
59 |
58
|
adantl |
|
60 |
45 51 48 57 59
|
ltletrd |
|
61 |
45 48 60
|
ltled |
|
62 |
61
|
adantlr |
|
63 |
47
|
adantl |
|
64 |
34
|
zred |
|
65 |
64
|
adantr |
|
66 |
|
elfzel2 |
|
67 |
66
|
zred |
|
68 |
67
|
adantr |
|
69 |
|
elfzle2 |
|
70 |
69
|
adantl |
|
71 |
|
elfzle2 |
|
72 |
71
|
adantr |
|
73 |
63 65 68 70 72
|
letrd |
|
74 |
73
|
adantll |
|
75 |
46
|
adantl |
|
76 |
|
0zd |
|
77 |
66
|
ad2antlr |
|
78 |
|
elfz |
|
79 |
75 76 77 78
|
syl3anc |
|
80 |
62 74 79
|
mpbir2and |
|
81 |
80
|
adantlll |
|
82 |
44 81
|
ffvelrnd |
|
83 |
82
|
adantlr |
|
84 |
|
simp-4l |
|
85 |
|
0red |
|
86 |
|
elfzelz |
|
87 |
86
|
zred |
|
88 |
87
|
adantl |
|
89 |
|
0red |
|
90 |
50
|
adantr |
|
91 |
87
|
adantl |
|
92 |
|
0red |
|
93 |
52
|
ltp1d |
|
94 |
92 52 50 54 93
|
lelttrd |
|
95 |
94
|
adantr |
|
96 |
|
elfzle1 |
|
97 |
96
|
adantl |
|
98 |
89 90 91 95 97
|
ltletrd |
|
99 |
98
|
adantlr |
|
100 |
85 88 99
|
ltled |
|
101 |
100
|
adantlll |
|
102 |
101
|
adantlr |
|
103 |
87
|
adantl |
|
104 |
|
peano2rem |
|
105 |
64 104
|
syl |
|
106 |
105
|
adantr |
|
107 |
67
|
adantr |
|
108 |
|
elfzle2 |
|
109 |
108
|
adantl |
|
110 |
|
zlem1lt |
|
111 |
34 66 110
|
syl2anc |
|
112 |
71 111
|
mpbid |
|
113 |
112
|
adantr |
|
114 |
103 106 107 109 113
|
lelttrd |
|
115 |
114
|
adantlr |
|
116 |
115
|
adantlll |
|
117 |
86
|
adantl |
|
118 |
|
0zd |
|
119 |
66
|
ad3antlr |
|
120 |
|
elfzo |
|
121 |
117 118 119 120
|
syl3anc |
|
122 |
102 116 121
|
mpbir2and |
|
123 |
16
|
adantr |
|
124 |
|
elfzofz |
|
125 |
124
|
adantl |
|
126 |
123 125
|
ffvelrnd |
|
127 |
|
fzofzp1 |
|
128 |
127
|
adantl |
|
129 |
123 128
|
ffvelrnd |
|
130 |
|
eleq1w |
|
131 |
130
|
anbi2d |
|
132 |
|
fveq2 |
|
133 |
|
oveq1 |
|
134 |
133
|
fveq2d |
|
135 |
132 134
|
breq12d |
|
136 |
131 135
|
imbi12d |
|
137 |
7
|
simprrd |
|
138 |
137
|
r19.21bi |
|
139 |
136 138
|
chvarvv |
|
140 |
126 129 139
|
ltled |
|
141 |
84 122 140
|
syl2anc |
|
142 |
43 83 141
|
monoord |
|
143 |
142
|
3adantl3 |
|
144 |
16
|
ffvelrnda |
|
145 |
144
|
3adant3 |
|
146 |
|
simp3 |
|
147 |
145 146
|
eqled |
|
148 |
147
|
3adant1r |
|
149 |
148
|
adantr |
|
150 |
22 30 27 143 149
|
letrd |
|
151 |
22 27 150
|
lensymd |
|
152 |
151
|
intnand |
|
153 |
64
|
ad2antlr |
|
154 |
52
|
ad3antlr |
|
155 |
|
simpr |
|
156 |
153 154 155
|
nltled |
|
157 |
156
|
3adantl3 |
|
158 |
|
eqcom |
|
159 |
158
|
biimpi |
|
160 |
159
|
adantr |
|
161 |
160
|
3ad2antl3 |
|
162 |
34
|
ad2antlr |
|
163 |
32
|
ad2antrr |
|
164 |
|
simpr |
|
165 |
|
eluz2 |
|
166 |
162 163 164 165
|
syl3anbrc |
|
167 |
166
|
adantlll |
|
168 |
17
|
ad2antrr |
|
169 |
|
0zd |
|
170 |
66
|
ad2antlr |
|
171 |
|
elfzelz |
|
172 |
171
|
adantl |
|
173 |
169 170 172
|
3jca |
|
174 |
|
0red |
|
175 |
64
|
adantr |
|
176 |
171
|
zred |
|
177 |
176
|
adantl |
|
178 |
|
elfzle1 |
|
179 |
178
|
adantr |
|
180 |
|
elfzle1 |
|
181 |
180
|
adantl |
|
182 |
174 175 177 179 181
|
letrd |
|
183 |
182
|
adantll |
|
184 |
176
|
adantl |
|
185 |
|
elfzoel2 |
|
186 |
185
|
zred |
|
187 |
186
|
adantr |
|
188 |
52
|
adantr |
|
189 |
|
elfzle2 |
|
190 |
189
|
adantl |
|
191 |
|
elfzolt2 |
|
192 |
191
|
adantr |
|
193 |
184 188 187 190 192
|
lelttrd |
|
194 |
184 187 193
|
ltled |
|
195 |
194
|
adantlr |
|
196 |
173 183 195
|
jca32 |
|
197 |
196
|
adantlll |
|
198 |
|
elfz2 |
|
199 |
197 198
|
sylibr |
|
200 |
168 199
|
ffvelrnd |
|
201 |
200
|
adantlr |
|
202 |
|
simplll |
|
203 |
|
0red |
|
204 |
64
|
ad2antlr |
|
205 |
|
elfzelz |
|
206 |
205
|
zred |
|
207 |
206
|
adantl |
|
208 |
178
|
ad2antlr |
|
209 |
|
elfzle1 |
|
210 |
209
|
adantl |
|
211 |
203 204 207 208 210
|
letrd |
|
212 |
206
|
adantl |
|
213 |
52
|
adantr |
|
214 |
186
|
adantr |
|
215 |
|
peano2rem |
|
216 |
213 215
|
syl |
|
217 |
|
elfzle2 |
|
218 |
217
|
adantl |
|
219 |
213
|
ltm1d |
|
220 |
212 216 213 218 219
|
lelttrd |
|
221 |
191
|
adantr |
|
222 |
212 213 214 220 221
|
lttrd |
|
223 |
222
|
adantlr |
|
224 |
205
|
adantl |
|
225 |
|
0zd |
|
226 |
185
|
ad2antrr |
|
227 |
224 225 226 120
|
syl3anc |
|
228 |
211 223 227
|
mpbir2and |
|
229 |
228
|
adantlll |
|
230 |
202 229 140
|
syl2anc |
|
231 |
230
|
adantlr |
|
232 |
167 201 231
|
monoord |
|
233 |
232
|
3adantl3 |
|
234 |
161 233
|
eqbrtrd |
|
235 |
25
|
adantr |
|
236 |
|
elfzofz |
|
237 |
236
|
adantl |
|
238 |
17 237
|
ffvelrnd |
|
239 |
235 238
|
lenltd |
|
240 |
239
|
adantr |
|
241 |
240
|
3ad2antl1 |
|
242 |
234 241
|
mpbid |
|
243 |
157 242
|
syldan |
|
244 |
243
|
intnanrd |
|
245 |
152 244
|
pm2.61dan |
|
246 |
245
|
intnand |
|
247 |
|
elioo3g |
|
248 |
246 247
|
sylnibr |
|
249 |
248
|
rexlimdv3a |
|
250 |
15 249
|
mpd |
|