Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem15.1 |
|
2 |
|
fourierdlem15.2 |
|
3 |
|
fourierdlem15.3 |
|
4 |
1
|
fourierdlem2 |
|
5 |
2 4
|
syl |
|
6 |
3 5
|
mpbid |
|
7 |
6
|
simpld |
|
8 |
|
reex |
|
9 |
8
|
a1i |
|
10 |
|
ovex |
|
11 |
10
|
a1i |
|
12 |
9 11
|
elmapd |
|
13 |
7 12
|
mpbid |
|
14 |
|
ffn |
|
15 |
13 14
|
syl |
|
16 |
6
|
simprd |
|
17 |
16
|
simpld |
|
18 |
17
|
simpld |
|
19 |
|
nnnn0 |
|
20 |
|
nn0uz |
|
21 |
19 20
|
eleqtrdi |
|
22 |
2 21
|
syl |
|
23 |
|
eluzfz1 |
|
24 |
22 23
|
syl |
|
25 |
13 24
|
ffvelrnd |
|
26 |
18 25
|
eqeltrrd |
|
27 |
26
|
adantr |
|
28 |
17
|
simprd |
|
29 |
|
eluzfz2 |
|
30 |
22 29
|
syl |
|
31 |
13 30
|
ffvelrnd |
|
32 |
28 31
|
eqeltrrd |
|
33 |
32
|
adantr |
|
34 |
13
|
ffvelrnda |
|
35 |
18
|
eqcomd |
|
36 |
35
|
adantr |
|
37 |
|
elfzuz |
|
38 |
37
|
adantl |
|
39 |
13
|
ad2antrr |
|
40 |
|
elfzle1 |
|
41 |
40
|
adantl |
|
42 |
|
elfzelz |
|
43 |
42
|
zred |
|
44 |
43
|
adantl |
|
45 |
|
elfzelz |
|
46 |
45
|
zred |
|
47 |
46
|
adantr |
|
48 |
|
elfzel2 |
|
49 |
48
|
zred |
|
50 |
49
|
adantr |
|
51 |
|
elfzle2 |
|
52 |
51
|
adantl |
|
53 |
|
elfzle2 |
|
54 |
53
|
adantr |
|
55 |
44 47 50 52 54
|
letrd |
|
56 |
42
|
adantl |
|
57 |
|
0zd |
|
58 |
48
|
adantr |
|
59 |
|
elfz |
|
60 |
56 57 58 59
|
syl3anc |
|
61 |
41 55 60
|
mpbir2and |
|
62 |
61
|
adantll |
|
63 |
39 62
|
ffvelrnd |
|
64 |
|
simpll |
|
65 |
|
elfzle1 |
|
66 |
65
|
adantl |
|
67 |
|
elfzelz |
|
68 |
67
|
zred |
|
69 |
68
|
adantl |
|
70 |
46
|
adantr |
|
71 |
49
|
adantr |
|
72 |
|
peano2rem |
|
73 |
70 72
|
syl |
|
74 |
|
elfzle2 |
|
75 |
74
|
adantl |
|
76 |
70
|
ltm1d |
|
77 |
69 73 70 75 76
|
lelttrd |
|
78 |
53
|
adantr |
|
79 |
69 70 71 77 78
|
ltletrd |
|
80 |
67
|
adantl |
|
81 |
|
0zd |
|
82 |
48
|
adantr |
|
83 |
|
elfzo |
|
84 |
80 81 82 83
|
syl3anc |
|
85 |
66 79 84
|
mpbir2and |
|
86 |
85
|
adantll |
|
87 |
13
|
adantr |
|
88 |
|
elfzofz |
|
89 |
88
|
adantl |
|
90 |
87 89
|
ffvelrnd |
|
91 |
|
fzofzp1 |
|
92 |
91
|
adantl |
|
93 |
87 92
|
ffvelrnd |
|
94 |
|
eleq1w |
|
95 |
94
|
anbi2d |
|
96 |
|
fveq2 |
|
97 |
|
oveq1 |
|
98 |
97
|
fveq2d |
|
99 |
96 98
|
breq12d |
|
100 |
95 99
|
imbi12d |
|
101 |
16
|
simprd |
|
102 |
101
|
r19.21bi |
|
103 |
100 102
|
chvarvv |
|
104 |
90 93 103
|
ltled |
|
105 |
64 86 104
|
syl2anc |
|
106 |
38 63 105
|
monoord |
|
107 |
36 106
|
eqbrtrd |
|
108 |
|
elfzuz3 |
|
109 |
108
|
adantl |
|
110 |
13
|
ad2antrr |
|
111 |
|
fz0fzelfz0 |
|
112 |
111
|
adantll |
|
113 |
110 112
|
ffvelrnd |
|
114 |
13
|
ad2antrr |
|
115 |
|
0red |
|
116 |
46
|
adantr |
|
117 |
|
elfzelz |
|
118 |
117
|
zred |
|
119 |
118
|
adantl |
|
120 |
|
elfzle1 |
|
121 |
120
|
adantr |
|
122 |
|
elfzle1 |
|
123 |
122
|
adantl |
|
124 |
115 116 119 121 123
|
letrd |
|
125 |
124
|
adantll |
|
126 |
118
|
adantl |
|
127 |
2
|
nnred |
|
128 |
127
|
adantr |
|
129 |
|
1red |
|
130 |
128 129
|
resubcld |
|
131 |
|
elfzle2 |
|
132 |
131
|
adantl |
|
133 |
128
|
ltm1d |
|
134 |
126 130 128 132 133
|
lelttrd |
|
135 |
126 128 134
|
ltled |
|
136 |
135
|
adantlr |
|
137 |
117
|
adantl |
|
138 |
|
0zd |
|
139 |
48
|
ad2antlr |
|
140 |
137 138 139 59
|
syl3anc |
|
141 |
125 136 140
|
mpbir2and |
|
142 |
114 141
|
ffvelrnd |
|
143 |
118
|
adantl |
|
144 |
|
1red |
|
145 |
|
0le1 |
|
146 |
145
|
a1i |
|
147 |
143 144 125 146
|
addge0d |
|
148 |
126 130 129 132
|
leadd1dd |
|
149 |
2
|
nncnd |
|
150 |
149
|
adantr |
|
151 |
|
1cnd |
|
152 |
150 151
|
npcand |
|
153 |
148 152
|
breqtrd |
|
154 |
153
|
adantlr |
|
155 |
137
|
peano2zd |
|
156 |
|
elfz |
|
157 |
155 138 139 156
|
syl3anc |
|
158 |
147 154 157
|
mpbir2and |
|
159 |
114 158
|
ffvelrnd |
|
160 |
|
simpll |
|
161 |
134
|
adantlr |
|
162 |
137 138 139 83
|
syl3anc |
|
163 |
125 161 162
|
mpbir2and |
|
164 |
160 163 103
|
syl2anc |
|
165 |
142 159 164
|
ltled |
|
166 |
109 113 165
|
monoord |
|
167 |
28
|
adantr |
|
168 |
166 167
|
breqtrd |
|
169 |
27 33 34 107 168
|
eliccd |
|
170 |
169
|
ralrimiva |
|
171 |
|
fnfvrnss |
|
172 |
15 170 171
|
syl2anc |
|
173 |
|
df-f |
|
174 |
15 172 173
|
sylanbrc |
|