Step |
Hyp |
Ref |
Expression |
1 |
|
quart1.a |
|
2 |
|
quart1.b |
|
3 |
|
quart1.c |
|
4 |
|
quart1.d |
|
5 |
|
quart1.p |
|
6 |
|
quart1.q |
|
7 |
|
quart1.r |
|
8 |
|
quart1.x |
|
9 |
|
quart1.y |
|
10 |
1 2
|
mulcld |
|
11 |
10
|
halfcld |
|
12 |
3 11
|
subcld |
|
13 |
|
3nn0 |
|
14 |
|
expcl |
|
15 |
1 13 14
|
sylancl |
|
16 |
|
8cn |
|
17 |
16
|
a1i |
|
18 |
|
8nn |
|
19 |
18
|
nnne0i |
|
20 |
19
|
a1i |
|
21 |
15 17 20
|
divcld |
|
22 |
|
4cn |
|
23 |
22
|
a1i |
|
24 |
|
4ne0 |
|
25 |
24
|
a1i |
|
26 |
1 23 25
|
divcld |
|
27 |
12 21 26
|
adddird |
|
28 |
6
|
oveq1d |
|
29 |
3 1 23 25
|
divassd |
|
30 |
1
|
sqvald |
|
31 |
30
|
oveq1d |
|
32 |
1 1 2
|
mul32d |
|
33 |
31 32
|
eqtrd |
|
34 |
33
|
oveq1d |
|
35 |
|
2cn |
|
36 |
|
4t2e8 |
|
37 |
22 35 36
|
mulcomli |
|
38 |
37
|
oveq2i |
|
39 |
34 38
|
eqtr4di |
|
40 |
35
|
a1i |
|
41 |
|
2ne0 |
|
42 |
41
|
a1i |
|
43 |
10 40 1 23 42 25
|
divmuldivd |
|
44 |
39 43
|
eqtr4d |
|
45 |
29 44
|
oveq12d |
|
46 |
3 11 26
|
subdird |
|
47 |
45 46
|
eqtr4d |
|
48 |
|
df-4 |
|
49 |
48
|
oveq2i |
|
50 |
|
expp1 |
|
51 |
1 13 50
|
sylancl |
|
52 |
49 51
|
syl5eq |
|
53 |
52
|
oveq1d |
|
54 |
15 1 17 20
|
div23d |
|
55 |
53 54
|
eqtrd |
|
56 |
55
|
oveq1d |
|
57 |
21 1 23 25
|
divassd |
|
58 |
56 57
|
eqtrd |
|
59 |
47 58
|
oveq12d |
|
60 |
27 28 59
|
3eqtr4d |
|
61 |
3 1
|
mulcld |
|
62 |
61 23 25
|
divcld |
|
63 |
1
|
sqcld |
|
64 |
63 2
|
mulcld |
|
65 |
64 17 20
|
divcld |
|
66 |
|
4nn0 |
|
67 |
|
expcl |
|
68 |
1 66 67
|
sylancl |
|
69 |
68 17 20
|
divcld |
|
70 |
69 23 25
|
divcld |
|
71 |
62 65 70
|
subadd23d |
|
72 |
70 65
|
subcld |
|
73 |
62 72
|
addcomd |
|
74 |
60 71 73
|
3eqtrd |
|
75 |
|
1nn0 |
|
76 |
|
6nn |
|
77 |
75 76
|
decnncl |
|
78 |
77
|
nncni |
|
79 |
78
|
a1i |
|
80 |
77
|
nnne0i |
|
81 |
80
|
a1i |
|
82 |
64 79 81
|
divcld |
|
83 |
|
3cn |
|
84 |
|
2nn0 |
|
85 |
|
5nn0 |
|
86 |
84 85
|
deccl |
|
87 |
86 76
|
decnncl |
|
88 |
87
|
nncni |
|
89 |
87
|
nnne0i |
|
90 |
83 88 89
|
divcli |
|
91 |
|
mulcl |
|
92 |
90 68 91
|
sylancr |
|
93 |
82 92
|
subcld |
|
94 |
4 93 62
|
addsubd |
|
95 |
7 94
|
eqtr4d |
|
96 |
74 95
|
oveq12d |
|
97 |
4 93
|
addcld |
|
98 |
72 62 97
|
ppncand |
|
99 |
72 4 93
|
add12d |
|
100 |
65 92
|
addcld |
|
101 |
70 82
|
addcld |
|
102 |
100 101
|
negsubdi2d |
|
103 |
70 82
|
addcomd |
|
104 |
103
|
oveq2d |
|
105 |
65 92 82 70
|
addsub4d |
|
106 |
83
|
a1i |
|
107 |
88
|
a1i |
|
108 |
89
|
a1i |
|
109 |
106 68 107 108
|
divassd |
|
110 |
106 68 107 108
|
div23d |
|
111 |
|
1p2e3 |
|
112 |
111
|
oveq1i |
|
113 |
|
1cnd |
|
114 |
68 107 108
|
divcld |
|
115 |
113 40 114
|
adddird |
|
116 |
112 115
|
eqtr3id |
|
117 |
114
|
mulid2d |
|
118 |
117
|
oveq1d |
|
119 |
116 118
|
eqtrd |
|
120 |
109 110 119
|
3eqtr3d |
|
121 |
48
|
oveq1i |
|
122 |
70 23 25
|
divcld |
|
123 |
106 113 122
|
adddird |
|
124 |
121 123
|
syl5eq |
|
125 |
70 23 25
|
divcan2d |
|
126 |
122
|
mulid2d |
|
127 |
69 23 23 25 25
|
divdiv1d |
|
128 |
|
4t4e16 |
|
129 |
128
|
oveq2i |
|
130 |
127 129
|
eqtrdi |
|
131 |
68 17 79 20 81
|
divdiv1d |
|
132 |
16 78
|
mulcli |
|
133 |
132
|
a1i |
|
134 |
16 78 19 80
|
mulne0i |
|
135 |
134
|
a1i |
|
136 |
68 133 135
|
divcld |
|
137 |
136 40 42
|
divcan2d |
|
138 |
68 133 40 135 42
|
divdiv1d |
|
139 |
16 78 35
|
mul32i |
|
140 |
|
2exp4 |
|
141 |
|
8t2e16 |
|
142 |
140 141
|
eqtr4i |
|
143 |
142 140
|
oveq12i |
|
144 |
|
4p4e8 |
|
145 |
144
|
oveq2i |
|
146 |
|
expadd |
|
147 |
35 66 66 146
|
mp3an |
|
148 |
|
2exp8 |
|
149 |
145 147 148
|
3eqtr3i |
|
150 |
139 143 149
|
3eqtr2i |
|
151 |
150
|
oveq2i |
|
152 |
138 151
|
eqtrdi |
|
153 |
152
|
oveq2d |
|
154 |
131 137 153
|
3eqtr2d |
|
155 |
126 130 154
|
3eqtrd |
|
156 |
155
|
oveq2d |
|
157 |
124 125 156
|
3eqtr3d |
|
158 |
120 157
|
oveq12d |
|
159 |
|
mulcl |
|
160 |
83 122 159
|
sylancr |
|
161 |
|
mulcl |
|
162 |
35 114 161
|
sylancr |
|
163 |
114 160 162
|
pnpcan2d |
|
164 |
158 163
|
eqtrd |
|
165 |
164
|
oveq2d |
|
166 |
82 114 160
|
addsub12d |
|
167 |
165 166
|
eqtrd |
|
168 |
64 17 40 20 42
|
divdiv1d |
|
169 |
141
|
oveq2i |
|
170 |
168 169
|
eqtrdi |
|
171 |
170
|
oveq2d |
|
172 |
65 40 42
|
divcan2d |
|
173 |
82
|
2timesd |
|
174 |
171 172 173
|
3eqtr3d |
|
175 |
82 82 174
|
mvrladdd |
|
176 |
175
|
oveq1d |
|
177 |
5
|
oveq1d |
|
178 |
83 16 19
|
divcli |
|
179 |
|
mulcl |
|
180 |
178 63 179
|
sylancr |
|
181 |
26
|
sqcld |
|
182 |
2 180 181
|
subdird |
|
183 |
1 23 25
|
sqdivd |
|
184 |
22
|
sqvali |
|
185 |
184 128
|
eqtri |
|
186 |
185
|
oveq2i |
|
187 |
183 186
|
eqtrdi |
|
188 |
187
|
oveq2d |
|
189 |
2 63 79 81
|
divassd |
|
190 |
2 63
|
mulcomd |
|
191 |
190
|
oveq1d |
|
192 |
188 189 191
|
3eqtr2d |
|
193 |
178
|
a1i |
|
194 |
193 63 63
|
mulassd |
|
195 |
106 68 17 20
|
div23d |
|
196 |
|
2p2e4 |
|
197 |
196
|
oveq2i |
|
198 |
84
|
a1i |
|
199 |
1 198 198
|
expaddd |
|
200 |
197 199
|
eqtr3id |
|
201 |
200
|
oveq2d |
|
202 |
195 201
|
eqtrd |
|
203 |
106 68 17 20
|
divassd |
|
204 |
194 202 203
|
3eqtr2d |
|
205 |
204
|
oveq1d |
|
206 |
185 79
|
eqeltrid |
|
207 |
185 80
|
eqnetri |
|
208 |
207
|
a1i |
|
209 |
180 63 206 208
|
divassd |
|
210 |
106 69 206 208
|
divassd |
|
211 |
205 209 210
|
3eqtr3d |
|
212 |
183
|
oveq2d |
|
213 |
185
|
oveq2i |
|
214 |
130 213
|
eqtr4di |
|
215 |
214
|
oveq2d |
|
216 |
211 212 215
|
3eqtr4d |
|
217 |
192 216
|
oveq12d |
|
218 |
177 182 217
|
3eqtrd |
|
219 |
218
|
oveq2d |
|
220 |
167 176 219
|
3eqtr4d |
|
221 |
104 105 220
|
3eqtrd |
|
222 |
221
|
negeqd |
|
223 |
70 82 65 92
|
addsub4d |
|
224 |
102 222 223
|
3eqtr3rd |
|
225 |
224
|
oveq2d |
|
226 |
2 180
|
subcld |
|
227 |
5 226
|
eqeltrd |
|
228 |
227 181
|
mulcld |
|
229 |
114 228
|
addcld |
|
230 |
4 229
|
negsubd |
|
231 |
99 225 230
|
3eqtrd |
|
232 |
96 98 231
|
3eqtrd |
|
233 |
232
|
oveq2d |
|
234 |
229 4
|
pncan3d |
|
235 |
233 234
|
eqtr2d |
|