Step |
Hyp |
Ref |
Expression |
1 |
|
seqf1o.1 |
|
2 |
|
seqf1o.2 |
|
3 |
|
seqf1o.3 |
|
4 |
|
seqf1o.4 |
|
5 |
|
seqf1o.5 |
|
6 |
|
seqf1olem.5 |
|
7 |
|
seqf1olem.6 |
|
8 |
|
seqf1olem.7 |
|
9 |
|
seqf1olem.8 |
|
10 |
|
fvexd |
|
11 |
|
fvex |
|
12 |
|
ovex |
|
13 |
11 12
|
ifex |
|
14 |
13
|
a1i |
|
15 |
|
iftrue |
|
16 |
15
|
fveq2d |
|
17 |
16
|
eqeq2d |
|
18 |
17
|
adantl |
|
19 |
|
simprr |
|
20 |
|
elfzelz |
|
21 |
20
|
zred |
|
22 |
21
|
ad2antlr |
|
23 |
|
simprl |
|
24 |
22 23
|
gtned |
|
25 |
|
f1of |
|
26 |
6 25
|
syl |
|
27 |
26
|
ad2antrr |
|
28 |
|
fzssp1 |
|
29 |
|
simplr |
|
30 |
28 29
|
sseldi |
|
31 |
27 30
|
ffvelrnd |
|
32 |
|
elfzp1 |
|
33 |
4 32
|
syl |
|
34 |
33
|
ad2antrr |
|
35 |
31 34
|
mpbid |
|
36 |
35
|
ord |
|
37 |
6
|
ad2antrr |
|
38 |
|
f1ocnvfv |
|
39 |
37 30 38
|
syl2anc |
|
40 |
9
|
eqeq1i |
|
41 |
39 40
|
syl6ibr |
|
42 |
36 41
|
syld |
|
43 |
42
|
necon1ad |
|
44 |
24 43
|
mpd |
|
45 |
19 44
|
eqeltrd |
|
46 |
19
|
eqcomd |
|
47 |
|
f1ocnvfv |
|
48 |
37 30 47
|
syl2anc |
|
49 |
46 48
|
mpd |
|
50 |
49 23
|
eqbrtrd |
|
51 |
|
iftrue |
|
52 |
50 51
|
syl |
|
53 |
52 49
|
eqtr2d |
|
54 |
45 53
|
jca |
|
55 |
54
|
expr |
|
56 |
18 55
|
sylbid |
|
57 |
|
iffalse |
|
58 |
57
|
fveq2d |
|
59 |
58
|
eqeq2d |
|
60 |
59
|
adantl |
|
61 |
|
simprr |
|
62 |
|
f1ocnv |
|
63 |
6 62
|
syl |
|
64 |
|
f1of1 |
|
65 |
63 64
|
syl |
|
66 |
|
f1f |
|
67 |
65 66
|
syl |
|
68 |
|
peano2uz |
|
69 |
4 68
|
syl |
|
70 |
|
eluzfz2 |
|
71 |
69 70
|
syl |
|
72 |
67 71
|
ffvelrnd |
|
73 |
9 72
|
eqeltrid |
|
74 |
|
elfzelz |
|
75 |
73 74
|
syl |
|
76 |
75
|
zred |
|
77 |
76
|
ad2antrr |
|
78 |
21
|
ad2antlr |
|
79 |
|
peano2re |
|
80 |
78 79
|
syl |
|
81 |
|
simprl |
|
82 |
77 78 81
|
nltled |
|
83 |
78
|
ltp1d |
|
84 |
77 78 80 82 83
|
lelttrd |
|
85 |
77 84
|
ltned |
|
86 |
26
|
ad2antrr |
|
87 |
|
fzp1elp1 |
|
88 |
87
|
ad2antlr |
|
89 |
86 88
|
ffvelrnd |
|
90 |
|
elfzp1 |
|
91 |
4 90
|
syl |
|
92 |
91
|
ad2antrr |
|
93 |
89 92
|
mpbid |
|
94 |
93
|
ord |
|
95 |
6
|
ad2antrr |
|
96 |
|
f1ocnvfv |
|
97 |
95 88 96
|
syl2anc |
|
98 |
9
|
eqeq1i |
|
99 |
97 98
|
syl6ibr |
|
100 |
94 99
|
syld |
|
101 |
100
|
necon1ad |
|
102 |
85 101
|
mpd |
|
103 |
61 102
|
eqeltrd |
|
104 |
61
|
eqcomd |
|
105 |
|
f1ocnvfv |
|
106 |
95 88 105
|
syl2anc |
|
107 |
104 106
|
mpd |
|
108 |
107
|
breq1d |
|
109 |
|
lttr |
|
110 |
78 80 77 109
|
syl3anc |
|
111 |
83 110
|
mpand |
|
112 |
108 111
|
sylbid |
|
113 |
81 112
|
mtod |
|
114 |
|
iffalse |
|
115 |
113 114
|
syl |
|
116 |
107
|
oveq1d |
|
117 |
78
|
recnd |
|
118 |
|
ax-1cn |
|
119 |
|
pncan |
|
120 |
117 118 119
|
sylancl |
|
121 |
115 116 120
|
3eqtrrd |
|
122 |
103 121
|
jca |
|
123 |
122
|
expr |
|
124 |
60 123
|
sylbid |
|
125 |
56 124
|
pm2.61dan |
|
126 |
125
|
expimpd |
|
127 |
51
|
eqeq2d |
|
128 |
127
|
adantl |
|
129 |
|
simprr |
|
130 |
67
|
ad2antrr |
|
131 |
|
simplr |
|
132 |
28 131
|
sseldi |
|
133 |
130 132
|
ffvelrnd |
|
134 |
129 133
|
eqeltrd |
|
135 |
|
elfzle1 |
|
136 |
134 135
|
syl |
|
137 |
|
elfzelz |
|
138 |
134 137
|
syl |
|
139 |
138
|
zred |
|
140 |
76
|
ad2antrr |
|
141 |
|
eluzelz |
|
142 |
4 141
|
syl |
|
143 |
142
|
peano2zd |
|
144 |
143
|
zred |
|
145 |
144
|
ad2antrr |
|
146 |
|
simprl |
|
147 |
129 146
|
eqbrtrd |
|
148 |
|
elfzle2 |
|
149 |
73 148
|
syl |
|
150 |
149
|
ad2antrr |
|
151 |
139 140 145 147 150
|
ltletrd |
|
152 |
142
|
ad2antrr |
|
153 |
|
zleltp1 |
|
154 |
138 152 153
|
syl2anc |
|
155 |
151 154
|
mpbird |
|
156 |
|
eluzel2 |
|
157 |
4 156
|
syl |
|
158 |
157
|
ad2antrr |
|
159 |
|
elfz |
|
160 |
138 158 152 159
|
syl3anc |
|
161 |
136 155 160
|
mpbir2and |
|
162 |
147 16
|
syl |
|
163 |
129
|
fveq2d |
|
164 |
6
|
ad2antrr |
|
165 |
|
f1ocnvfv2 |
|
166 |
164 132 165
|
syl2anc |
|
167 |
162 163 166
|
3eqtrrd |
|
168 |
161 167
|
jca |
|
169 |
168
|
expr |
|
170 |
128 169
|
sylbid |
|
171 |
114
|
eqeq2d |
|
172 |
171
|
adantl |
|
173 |
157
|
zred |
|
174 |
173
|
ad2antrr |
|
175 |
76
|
ad2antrr |
|
176 |
|
simprr |
|
177 |
67
|
ad2antrr |
|
178 |
|
simplr |
|
179 |
28 178
|
sseldi |
|
180 |
177 179
|
ffvelrnd |
|
181 |
|
elfzelz |
|
182 |
180 181
|
syl |
|
183 |
|
peano2zm |
|
184 |
182 183
|
syl |
|
185 |
176 184
|
eqeltrd |
|
186 |
185
|
zred |
|
187 |
|
elfzle1 |
|
188 |
73 187
|
syl |
|
189 |
188
|
ad2antrr |
|
190 |
182
|
zred |
|
191 |
|
simprl |
|
192 |
175 190 191
|
nltled |
|
193 |
|
elfzelz |
|
194 |
193
|
adantl |
|
195 |
194
|
zred |
|
196 |
142
|
zred |
|
197 |
196
|
adantr |
|
198 |
144
|
adantr |
|
199 |
|
elfzle2 |
|
200 |
199
|
adantl |
|
201 |
197
|
ltp1d |
|
202 |
195 197 198 200 201
|
lelttrd |
|
203 |
195 202
|
gtned |
|
204 |
203
|
adantr |
|
205 |
65
|
ad2antrr |
|
206 |
71
|
ad2antrr |
|
207 |
|
f1fveq |
|
208 |
205 206 179 207
|
syl12anc |
|
209 |
208
|
necon3bid |
|
210 |
204 209
|
mpbird |
|
211 |
9
|
neeq1i |
|
212 |
210 211
|
sylibr |
|
213 |
212
|
necomd |
|
214 |
175 190 192 213
|
leneltd |
|
215 |
75
|
ad2antrr |
|
216 |
|
zltlem1 |
|
217 |
215 182 216
|
syl2anc |
|
218 |
214 217
|
mpbid |
|
219 |
218 176
|
breqtrrd |
|
220 |
174 175 186 189 219
|
letrd |
|
221 |
|
elfzle2 |
|
222 |
180 221
|
syl |
|
223 |
196
|
ad2antrr |
|
224 |
|
1re |
|
225 |
|
lesubadd |
|
226 |
224 225
|
mp3an2 |
|
227 |
190 223 226
|
syl2anc |
|
228 |
222 227
|
mpbird |
|
229 |
176 228
|
eqbrtrd |
|
230 |
157
|
ad2antrr |
|
231 |
142
|
ad2antrr |
|
232 |
185 230 231 159
|
syl3anc |
|
233 |
220 229 232
|
mpbir2and |
|
234 |
175 186 219
|
lensymd |
|
235 |
234 58
|
syl |
|
236 |
176
|
oveq1d |
|
237 |
182
|
zcnd |
|
238 |
|
npcan |
|
239 |
237 118 238
|
sylancl |
|
240 |
236 239
|
eqtrd |
|
241 |
240
|
fveq2d |
|
242 |
6
|
ad2antrr |
|
243 |
242 179 165
|
syl2anc |
|
244 |
235 241 243
|
3eqtrrd |
|
245 |
233 244
|
jca |
|
246 |
245
|
expr |
|
247 |
172 246
|
sylbid |
|
248 |
170 247
|
pm2.61dan |
|
249 |
248
|
expimpd |
|
250 |
126 249
|
impbid |
|
251 |
8 10 14 250
|
f1od |
|