Step |
Hyp |
Ref |
Expression |
1 |
|
psgnunilem2.g |
|
2 |
|
psgnunilem2.t |
|
3 |
|
psgnunilem2.d |
|
4 |
|
psgnunilem2.w |
|
5 |
|
psgnunilem2.id |
|
6 |
|
psgnunilem2.l |
|
7 |
|
psgnunilem2.ix |
|
8 |
|
psgnunilem2.a |
|
9 |
|
psgnunilem2.al |
|
10 |
|
psgnunilem2.in |
|
11 |
|
wrd0 |
|
12 |
|
splcl |
|
13 |
4 11 12
|
sylancl |
|
14 |
13
|
adantr |
|
15 |
|
fzossfz |
|
16 |
15 7
|
sseldi |
|
17 |
|
elfznn0 |
|
18 |
16 17
|
syl |
|
19 |
|
2nn0 |
|
20 |
|
nn0addcl |
|
21 |
18 19 20
|
sylancl |
|
22 |
18
|
nn0red |
|
23 |
|
nn0addge1 |
|
24 |
22 19 23
|
sylancl |
|
25 |
|
elfz2nn0 |
|
26 |
18 21 24 25
|
syl3anbrc |
|
27 |
1 2 3 4 5 6 7 8 9
|
psgnunilem5 |
|
28 |
|
fzofzp1 |
|
29 |
27 28
|
syl |
|
30 |
|
df-2 |
|
31 |
30
|
oveq2i |
|
32 |
18
|
nn0cnd |
|
33 |
|
1cnd |
|
34 |
32 33 33
|
addassd |
|
35 |
31 34
|
eqtr4id |
|
36 |
6
|
oveq2d |
|
37 |
29 35 36
|
3eltr4d |
|
38 |
11
|
a1i |
|
39 |
4 26 37 38
|
spllen |
|
40 |
|
hash0 |
|
41 |
40
|
oveq1i |
|
42 |
|
df-neg |
|
43 |
41 42
|
eqtr4i |
|
44 |
|
2cn |
|
45 |
|
pncan2 |
|
46 |
32 44 45
|
sylancl |
|
47 |
46
|
negeqd |
|
48 |
43 47
|
syl5eq |
|
49 |
6 48
|
oveq12d |
|
50 |
|
elfzel2 |
|
51 |
16 50
|
syl |
|
52 |
51
|
zcnd |
|
53 |
|
negsub |
|
54 |
52 44 53
|
sylancl |
|
55 |
39 49 54
|
3eqtrd |
|
56 |
55
|
adantr |
|
57 |
|
splid |
|
58 |
4 26 37 57
|
syl12anc |
|
59 |
58
|
oveq2d |
|
60 |
59
|
adantr |
|
61 |
|
eqid |
|
62 |
1
|
symggrp |
|
63 |
3 62
|
syl |
|
64 |
|
grpmnd |
|
65 |
63 64
|
syl |
|
66 |
65
|
adantr |
|
67 |
2 1 61
|
symgtrf |
|
68 |
|
sswrd |
|
69 |
67 68
|
ax-mp |
|
70 |
69 4
|
sseldi |
|
71 |
70
|
adantr |
|
72 |
26
|
adantr |
|
73 |
37
|
adantr |
|
74 |
|
swrdcl |
|
75 |
70 74
|
syl |
|
76 |
75
|
adantr |
|
77 |
|
wrd0 |
|
78 |
77
|
a1i |
|
79 |
6
|
oveq2d |
|
80 |
27 79
|
eleqtrrd |
|
81 |
|
swrds2 |
|
82 |
4 18 80 81
|
syl3anc |
|
83 |
82
|
oveq2d |
|
84 |
|
wrdf |
|
85 |
4 84
|
syl |
|
86 |
79
|
feq2d |
|
87 |
85 86
|
mpbid |
|
88 |
87 7
|
ffvelrnd |
|
89 |
67 88
|
sseldi |
|
90 |
87 27
|
ffvelrnd |
|
91 |
67 90
|
sseldi |
|
92 |
|
eqid |
|
93 |
61 92
|
gsumws2 |
|
94 |
65 89 91 93
|
syl3anc |
|
95 |
1 61 92
|
symgov |
|
96 |
89 91 95
|
syl2anc |
|
97 |
83 94 96
|
3eqtrd |
|
98 |
97
|
adantr |
|
99 |
|
simpr |
|
100 |
1
|
symgid |
|
101 |
3 100
|
syl |
|
102 |
|
eqid |
|
103 |
102
|
gsum0 |
|
104 |
101 103
|
eqtr4di |
|
105 |
104
|
adantr |
|
106 |
98 99 105
|
3eqtrd |
|
107 |
61 66 71 72 73 76 78 106
|
gsumspl |
|
108 |
5
|
adantr |
|
109 |
60 107 108
|
3eqtr3d |
|
110 |
|
fveqeq2 |
|
111 |
|
oveq2 |
|
112 |
111
|
eqeq1d |
|
113 |
110 112
|
anbi12d |
|
114 |
113
|
rspcev |
|
115 |
14 56 109 114
|
syl12anc |
|
116 |
10
|
adantr |
|
117 |
115 116
|
pm2.21dd |
|
118 |
117
|
ex |
|
119 |
4
|
adantr |
|
120 |
|
simprl |
|
121 |
|
simprr |
|
122 |
120 121
|
s2cld |
|
123 |
|
splcl |
|
124 |
119 122 123
|
syl2anc |
|
125 |
124
|
adantrr |
|
126 |
65
|
adantr |
|
127 |
70
|
adantr |
|
128 |
26
|
adantr |
|
129 |
37
|
adantr |
|
130 |
69 122
|
sseldi |
|
131 |
130
|
adantrr |
|
132 |
75
|
adantr |
|
133 |
|
simprr1 |
|
134 |
97
|
adantr |
|
135 |
65
|
adantr |
|
136 |
67
|
a1i |
|
137 |
136
|
sselda |
|
138 |
137
|
adantrr |
|
139 |
136
|
sselda |
|
140 |
139
|
adantrl |
|
141 |
61 92
|
gsumws2 |
|
142 |
135 138 140 141
|
syl3anc |
|
143 |
1 61 92
|
symgov |
|
144 |
138 140 143
|
syl2anc |
|
145 |
142 144
|
eqtrd |
|
146 |
145
|
adantrr |
|
147 |
133 134 146
|
3eqtr4rd |
|
148 |
61 126 127 128 129 131 132 147
|
gsumspl |
|
149 |
59
|
adantr |
|
150 |
5
|
adantr |
|
151 |
148 149 150
|
3eqtrd |
|
152 |
26
|
adantr |
|
153 |
37
|
adantr |
|
154 |
119 152 153 122
|
spllen |
|
155 |
|
s2len |
|
156 |
155
|
oveq1i |
|
157 |
46
|
oveq2d |
|
158 |
44
|
subidi |
|
159 |
157 158
|
eqtrdi |
|
160 |
156 159
|
syl5eq |
|
161 |
160
|
oveq2d |
|
162 |
6 52
|
eqeltrd |
|
163 |
162
|
addid1d |
|
164 |
161 163 6
|
3eqtrd |
|
165 |
164
|
adantr |
|
166 |
154 165
|
eqtrd |
|
167 |
166
|
adantrr |
|
168 |
151 167
|
jca |
|
169 |
27
|
adantr |
|
170 |
|
simprr2 |
|
171 |
|
1nn0 |
|
172 |
|
2nn |
|
173 |
|
1lt2 |
|
174 |
|
elfzo0 |
|
175 |
171 172 173 174
|
mpbir3an |
|
176 |
155
|
oveq2i |
|
177 |
175 176
|
eleqtrri |
|
178 |
177
|
a1i |
|
179 |
119 152 153 122 178
|
splfv2a |
|
180 |
|
s2fv1 |
|
181 |
180
|
ad2antll |
|
182 |
179 181
|
eqtrd |
|
183 |
182
|
adantrr |
|
184 |
183
|
difeq1d |
|
185 |
184
|
dmeqd |
|
186 |
170 185
|
eleqtrrd |
|
187 |
|
fzosplitsni |
|
188 |
|
nn0uz |
|
189 |
187 188
|
eleq2s |
|
190 |
18 189
|
syl |
|
191 |
190
|
adantr |
|
192 |
|
fveq2 |
|
193 |
192
|
difeq1d |
|
194 |
193
|
dmeqd |
|
195 |
194
|
eleq2d |
|
196 |
195
|
notbid |
|
197 |
196
|
rspccva |
|
198 |
9 197
|
sylan |
|
199 |
198
|
adantlr |
|
200 |
4
|
ad2antrr |
|
201 |
26
|
ad2antrr |
|
202 |
37
|
ad2antrr |
|
203 |
122
|
adantr |
|
204 |
|
simpr |
|
205 |
200 201 202 203 204
|
splfv1 |
|
206 |
205
|
difeq1d |
|
207 |
206
|
dmeqd |
|
208 |
199 207
|
neleqtrrd |
|
209 |
208
|
ex |
|
210 |
209
|
adantrr |
|
211 |
|
simprr3 |
|
212 |
|
0nn0 |
|
213 |
|
2pos |
|
214 |
|
elfzo0 |
|
215 |
212 172 213 214
|
mpbir3an |
|
216 |
215 176
|
eleqtrri |
|
217 |
216
|
a1i |
|
218 |
119 152 153 122 217
|
splfv2a |
|
219 |
32
|
addid1d |
|
220 |
219
|
adantr |
|
221 |
220
|
fveq2d |
|
222 |
|
s2fv0 |
|
223 |
222
|
ad2antrl |
|
224 |
218 221 223
|
3eqtr3d |
|
225 |
224
|
difeq1d |
|
226 |
225
|
dmeqd |
|
227 |
226
|
eleq2d |
|
228 |
227
|
adantrr |
|
229 |
211 228
|
mtbird |
|
230 |
|
fveq2 |
|
231 |
230
|
difeq1d |
|
232 |
231
|
dmeqd |
|
233 |
232
|
eleq2d |
|
234 |
233
|
notbid |
|
235 |
229 234
|
syl5ibrcom |
|
236 |
210 235
|
jaod |
|
237 |
191 236
|
sylbid |
|
238 |
237
|
ralrimiv |
|
239 |
169 186 238
|
3jca |
|
240 |
|
oveq2 |
|
241 |
240
|
eqeq1d |
|
242 |
|
fveqeq2 |
|
243 |
241 242
|
anbi12d |
|
244 |
|
fveq1 |
|
245 |
244
|
difeq1d |
|
246 |
245
|
dmeqd |
|
247 |
246
|
eleq2d |
|
248 |
|
fveq1 |
|
249 |
248
|
difeq1d |
|
250 |
249
|
dmeqd |
|
251 |
250
|
eleq2d |
|
252 |
251
|
notbid |
|
253 |
252
|
ralbidv |
|
254 |
247 253
|
3anbi23d |
|
255 |
243 254
|
anbi12d |
|
256 |
255
|
rspcev |
|
257 |
125 168 239 256
|
syl12anc |
|
258 |
257
|
expr |
|
259 |
258
|
rexlimdvva |
|
260 |
2 3 88 90 8
|
psgnunilem1 |
|
261 |
118 259 260
|
mpjaod |
|