Step |
Hyp |
Ref |
Expression |
1 |
|
2sq.1 |
|
2 |
|
2sqlem7.2 |
|
3 |
|
2sqlem9.5 |
|
4 |
|
2sqlem9.7 |
|
5 |
|
2sqlem8.n |
|
6 |
|
2sqlem8.m |
|
7 |
|
2sqlem8.1 |
|
8 |
|
2sqlem8.2 |
|
9 |
|
2sqlem8.3 |
|
10 |
|
2sqlem8.4 |
|
11 |
|
2sqlem8.c |
|
12 |
|
2sqlem8.d |
|
13 |
|
2sqlem8.e |
|
14 |
|
2sqlem8.f |
|
15 |
|
eluz2b3 |
|
16 |
6 15
|
sylib |
|
17 |
16
|
simpld |
|
18 |
|
eluzelz |
|
19 |
6 18
|
syl |
|
20 |
5
|
nnzd |
|
21 |
7 17 11
|
4sqlem5 |
|
22 |
21
|
simpld |
|
23 |
|
zsqcl |
|
24 |
22 23
|
syl |
|
25 |
8 17 12
|
4sqlem5 |
|
26 |
25
|
simpld |
|
27 |
|
zsqcl |
|
28 |
26 27
|
syl |
|
29 |
24 28
|
zaddcld |
|
30 |
|
zsqcl |
|
31 |
7 30
|
syl |
|
32 |
31 24
|
zsubcld |
|
33 |
|
zsqcl |
|
34 |
8 33
|
syl |
|
35 |
34 28
|
zsubcld |
|
36 |
7 17 11
|
4sqlem8 |
|
37 |
8 17 12
|
4sqlem8 |
|
38 |
19 32 35 36 37
|
dvds2addd |
|
39 |
10
|
oveq1d |
|
40 |
31
|
zcnd |
|
41 |
34
|
zcnd |
|
42 |
24
|
zcnd |
|
43 |
28
|
zcnd |
|
44 |
40 41 42 43
|
addsub4d |
|
45 |
39 44
|
eqtrd |
|
46 |
38 45
|
breqtrrd |
|
47 |
|
dvdssub2 |
|
48 |
19 20 29 46 47
|
syl31anc |
|
49 |
4 48
|
mpbid |
|
50 |
1 2 3 4 5 6 7 8 9 10 11 12
|
2sqlem8a |
|
51 |
50
|
nnzd |
|
52 |
|
zsqcl2 |
|
53 |
51 52
|
syl |
|
54 |
53
|
nn0cnd |
|
55 |
|
gcddvds |
|
56 |
22 26 55
|
syl2anc |
|
57 |
56
|
simpld |
|
58 |
50
|
nnne0d |
|
59 |
|
dvdsval2 |
|
60 |
51 58 22 59
|
syl3anc |
|
61 |
57 60
|
mpbid |
|
62 |
13 61
|
eqeltrid |
|
63 |
|
zsqcl2 |
|
64 |
62 63
|
syl |
|
65 |
64
|
nn0cnd |
|
66 |
56
|
simprd |
|
67 |
|
dvdsval2 |
|
68 |
51 58 26 67
|
syl3anc |
|
69 |
66 68
|
mpbid |
|
70 |
14 69
|
eqeltrid |
|
71 |
|
zsqcl2 |
|
72 |
70 71
|
syl |
|
73 |
72
|
nn0cnd |
|
74 |
54 65 73
|
adddid |
|
75 |
51
|
zcnd |
|
76 |
62
|
zcnd |
|
77 |
75 76
|
sqmuld |
|
78 |
13
|
oveq2i |
|
79 |
22
|
zcnd |
|
80 |
79 75 58
|
divcan2d |
|
81 |
78 80
|
syl5eq |
|
82 |
81
|
oveq1d |
|
83 |
77 82
|
eqtr3d |
|
84 |
70
|
zcnd |
|
85 |
75 84
|
sqmuld |
|
86 |
14
|
oveq2i |
|
87 |
26
|
zcnd |
|
88 |
87 75 58
|
divcan2d |
|
89 |
86 88
|
syl5eq |
|
90 |
89
|
oveq1d |
|
91 |
85 90
|
eqtr3d |
|
92 |
83 91
|
oveq12d |
|
93 |
74 92
|
eqtrd |
|
94 |
49 93
|
breqtrrd |
|
95 |
|
zsqcl |
|
96 |
51 95
|
syl |
|
97 |
19 96
|
gcdcomd |
|
98 |
51 19
|
gcdcld |
|
99 |
98
|
nn0zd |
|
100 |
|
gcddvds |
|
101 |
51 19 100
|
syl2anc |
|
102 |
101
|
simpld |
|
103 |
99 51 22 102 57
|
dvdstrd |
|
104 |
7 22
|
zsubcld |
|
105 |
101
|
simprd |
|
106 |
21
|
simprd |
|
107 |
17
|
nnne0d |
|
108 |
|
dvdsval2 |
|
109 |
19 107 104 108
|
syl3anc |
|
110 |
106 109
|
mpbird |
|
111 |
99 19 104 105 110
|
dvdstrd |
|
112 |
|
dvdssub2 |
|
113 |
99 7 22 111 112
|
syl31anc |
|
114 |
103 113
|
mpbird |
|
115 |
99 51 26 102 66
|
dvdstrd |
|
116 |
8 26
|
zsubcld |
|
117 |
25
|
simprd |
|
118 |
|
dvdsval2 |
|
119 |
19 107 116 118
|
syl3anc |
|
120 |
117 119
|
mpbird |
|
121 |
99 19 116 105 120
|
dvdstrd |
|
122 |
|
dvdssub2 |
|
123 |
99 8 26 121 122
|
syl31anc |
|
124 |
115 123
|
mpbird |
|
125 |
|
ax-1ne0 |
|
126 |
125
|
a1i |
|
127 |
9 126
|
eqnetrd |
|
128 |
127
|
neneqd |
|
129 |
|
gcdeq0 |
|
130 |
7 8 129
|
syl2anc |
|
131 |
128 130
|
mtbid |
|
132 |
|
dvdslegcd |
|
133 |
99 7 8 131 132
|
syl31anc |
|
134 |
114 124 133
|
mp2and |
|
135 |
134 9
|
breqtrd |
|
136 |
|
simpr |
|
137 |
136
|
necon3ai |
|
138 |
107 137
|
syl |
|
139 |
|
gcdn0cl |
|
140 |
51 19 138 139
|
syl21anc |
|
141 |
|
nnle1eq1 |
|
142 |
140 141
|
syl |
|
143 |
135 142
|
mpbid |
|
144 |
|
2nn |
|
145 |
144
|
a1i |
|
146 |
|
rplpwr |
|
147 |
50 17 145 146
|
syl3anc |
|
148 |
143 147
|
mpd |
|
149 |
97 148
|
eqtrd |
|
150 |
64 72
|
nn0addcld |
|
151 |
150
|
nn0zd |
|
152 |
|
coprmdvds |
|
153 |
19 96 151 152
|
syl3anc |
|
154 |
94 149 153
|
mp2and |
|
155 |
|
dvdsval2 |
|
156 |
19 107 151 155
|
syl3anc |
|
157 |
154 156
|
mpbid |
|
158 |
64
|
nn0red |
|
159 |
72
|
nn0red |
|
160 |
158 159
|
readdcld |
|
161 |
17
|
nnred |
|
162 |
1 2
|
2sqlem7 |
|
163 |
|
inss2 |
|
164 |
162 163
|
sstri |
|
165 |
62 70
|
gcdcld |
|
166 |
165
|
nn0cnd |
|
167 |
|
1cnd |
|
168 |
75
|
mulid1d |
|
169 |
81 89
|
oveq12d |
|
170 |
22 26
|
gcdcld |
|
171 |
|
mulgcd |
|
172 |
170 62 70 171
|
syl3anc |
|
173 |
168 169 172
|
3eqtr2rd |
|
174 |
166 167 75 58 173
|
mulcanad |
|
175 |
|
eqidd |
|
176 |
|
oveq1 |
|
177 |
176
|
eqeq1d |
|
178 |
|
oveq1 |
|
179 |
178
|
oveq1d |
|
180 |
179
|
eqeq2d |
|
181 |
177 180
|
anbi12d |
|
182 |
|
oveq2 |
|
183 |
182
|
eqeq1d |
|
184 |
|
oveq1 |
|
185 |
184
|
oveq2d |
|
186 |
185
|
eqeq2d |
|
187 |
183 186
|
anbi12d |
|
188 |
181 187
|
rspc2ev |
|
189 |
62 70 174 175 188
|
syl112anc |
|
190 |
|
ovex |
|
191 |
|
eqeq1 |
|
192 |
191
|
anbi2d |
|
193 |
192
|
2rexbidv |
|
194 |
190 193 2
|
elab2 |
|
195 |
189 194
|
sylibr |
|
196 |
164 195
|
sseldi |
|
197 |
196
|
nngt0d |
|
198 |
17
|
nngt0d |
|
199 |
160 161 197 198
|
divgt0d |
|
200 |
|
elnnz |
|
201 |
157 199 200
|
sylanbrc |
|
202 |
|
prmnn |
|
203 |
202
|
ad2antrl |
|
204 |
203
|
nnred |
|
205 |
157
|
adantr |
|
206 |
205
|
zred |
|
207 |
|
peano2zm |
|
208 |
19 207
|
syl |
|
209 |
208
|
zred |
|
210 |
209
|
adantr |
|
211 |
|
simprr |
|
212 |
|
prmz |
|
213 |
212
|
ad2antrl |
|
214 |
201
|
adantr |
|
215 |
|
dvdsle |
|
216 |
213 214 215
|
syl2anc |
|
217 |
211 216
|
mpd |
|
218 |
|
zsqcl |
|
219 |
19 218
|
syl |
|
220 |
219
|
zred |
|
221 |
220
|
rehalfcld |
|
222 |
24
|
zred |
|
223 |
28
|
zred |
|
224 |
222 223
|
readdcld |
|
225 |
|
1red |
|
226 |
50
|
nnsqcld |
|
227 |
226
|
nnred |
|
228 |
150
|
nn0ge0d |
|
229 |
226
|
nnge1d |
|
230 |
225 227 160 228 229
|
lemul1ad |
|
231 |
150
|
nn0cnd |
|
232 |
231
|
mulid2d |
|
233 |
230 232 93
|
3brtr3d |
|
234 |
221
|
rehalfcld |
|
235 |
7 17 11
|
4sqlem7 |
|
236 |
8 17 12
|
4sqlem7 |
|
237 |
222 223 234 234 235 236
|
le2addd |
|
238 |
221
|
recnd |
|
239 |
238
|
2halvesd |
|
240 |
237 239
|
breqtrd |
|
241 |
160 224 221 233 240
|
letrd |
|
242 |
17
|
nnsqcld |
|
243 |
242
|
nnrpd |
|
244 |
|
rphalflt |
|
245 |
243 244
|
syl |
|
246 |
160 221 220 241 245
|
lelttrd |
|
247 |
19
|
zcnd |
|
248 |
247
|
sqvald |
|
249 |
246 248
|
breqtrd |
|
250 |
|
ltdivmul |
|
251 |
160 161 161 198 250
|
syl112anc |
|
252 |
249 251
|
mpbird |
|
253 |
|
zltlem1 |
|
254 |
157 19 253
|
syl2anc |
|
255 |
252 254
|
mpbid |
|
256 |
255
|
adantr |
|
257 |
204 206 210 217 256
|
letrd |
|
258 |
208
|
adantr |
|
259 |
|
fznn |
|
260 |
258 259
|
syl |
|
261 |
203 257 260
|
mpbir2and |
|
262 |
195
|
adantr |
|
263 |
261 262
|
jca |
|
264 |
3
|
adantr |
|
265 |
151
|
adantr |
|
266 |
|
dvdsmul2 |
|
267 |
19 157 266
|
syl2anc |
|
268 |
231 247 107
|
divcan2d |
|
269 |
267 268
|
breqtrd |
|
270 |
269
|
adantr |
|
271 |
213 205 265 211 270
|
dvdstrd |
|
272 |
|
breq1 |
|
273 |
|
eleq1w |
|
274 |
272 273
|
imbi12d |
|
275 |
|
breq2 |
|
276 |
275
|
imbi1d |
|
277 |
274 276
|
rspc2v |
|
278 |
263 264 271 277
|
syl3c |
|
279 |
278
|
expr |
|
280 |
279
|
ralrimiva |
|
281 |
|
inss1 |
|
282 |
162 281
|
sstri |
|
283 |
282 195
|
sseldi |
|
284 |
268 283
|
eqeltrd |
|
285 |
1 17 201 280 284
|
2sqlem6 |
|