Step |
Hyp |
Ref |
Expression |
1 |
|
dquart.b |
|
2 |
|
dquart.c |
|
3 |
|
dquart.x |
|
4 |
|
dquart.s |
|
5 |
|
dquart.m |
|
6 |
|
dquart.m0 |
|
7 |
|
dquart.i |
|
8 |
|
dquart.i2 |
|
9 |
|
dquart.d |
|
10 |
|
dquart.3 |
|
11 |
|
dquart.j |
|
12 |
|
dquart.j2 |
|
13 |
3
|
sqcld |
|
14 |
|
2cn |
|
15 |
|
mulcl |
|
16 |
14 4 15
|
sylancr |
|
17 |
16
|
sqcld |
|
18 |
5 17
|
eqeltrd |
|
19 |
18 1
|
addcld |
|
20 |
19
|
halfcld |
|
21 |
|
binom2 |
|
22 |
13 20 21
|
syl2anc |
|
23 |
|
2t2e4 |
|
24 |
23
|
oveq2i |
|
25 |
|
2nn0 |
|
26 |
25
|
a1i |
|
27 |
3 26 26
|
expmuld |
|
28 |
24 27
|
syl5reqr |
|
29 |
14
|
a1i |
|
30 |
29 13 20
|
mul12d |
|
31 |
|
2ne0 |
|
32 |
31
|
a1i |
|
33 |
19 29 32
|
divcan2d |
|
34 |
33
|
oveq2d |
|
35 |
13 19
|
mulcomd |
|
36 |
34 35
|
eqtrd |
|
37 |
18 1 13
|
adddird |
|
38 |
30 36 37
|
3eqtrd |
|
39 |
28 38
|
oveq12d |
|
40 |
|
4nn0 |
|
41 |
|
expcl |
|
42 |
3 40 41
|
sylancl |
|
43 |
18 13
|
mulcld |
|
44 |
1 13
|
mulcld |
|
45 |
42 43 44
|
add12d |
|
46 |
39 45
|
eqtrd |
|
47 |
46
|
oveq1d |
|
48 |
42 44
|
addcld |
|
49 |
20
|
sqcld |
|
50 |
43 48 49
|
addassd |
|
51 |
22 47 50
|
3eqtrd |
|
52 |
18
|
halfcld |
|
53 |
52 3
|
mulcld |
|
54 |
|
4cn |
|
55 |
54
|
a1i |
|
56 |
|
4ne0 |
|
57 |
56
|
a1i |
|
58 |
2 55 57
|
divcld |
|
59 |
53 58
|
subcld |
|
60 |
5 6
|
eqnetrrd |
|
61 |
|
sqne0 |
|
62 |
16 61
|
syl |
|
63 |
60 62
|
mpbid |
|
64 |
|
mulne0b |
|
65 |
14 4 64
|
sylancr |
|
66 |
63 65
|
mpbird |
|
67 |
66
|
simprd |
|
68 |
59 4 29 67 32
|
divcan5d |
|
69 |
29 53 58
|
subdid |
|
70 |
29 52 3
|
mulassd |
|
71 |
18 29 32
|
divcan2d |
|
72 |
71
|
oveq1d |
|
73 |
70 72
|
eqtr3d |
|
74 |
29 2 55 57
|
divassd |
|
75 |
23
|
oveq2i |
|
76 |
2 29 29 32 32
|
divcan5d |
|
77 |
75 76
|
eqtr3id |
|
78 |
74 77
|
eqtr3d |
|
79 |
73 78
|
oveq12d |
|
80 |
69 79
|
eqtrd |
|
81 |
80
|
oveq1d |
|
82 |
68 81
|
eqtr3d |
|
83 |
82
|
oveq1d |
|
84 |
18 3
|
mulcld |
|
85 |
2
|
halfcld |
|
86 |
84 85
|
subcld |
|
87 |
86 16 63
|
sqdivd |
|
88 |
18
|
sqcld |
|
89 |
88 13
|
mulcld |
|
90 |
84 2
|
mulcld |
|
91 |
89 90
|
subcld |
|
92 |
2
|
sqcld |
|
93 |
92 55 57
|
divcld |
|
94 |
91 93 18 6
|
divdird |
|
95 |
|
binom2sub |
|
96 |
84 85 95
|
syl2anc |
|
97 |
18 3
|
sqmuld |
|
98 |
29 84 85
|
mul12d |
|
99 |
2 29 32
|
divcan2d |
|
100 |
99
|
oveq2d |
|
101 |
98 100
|
eqtrd |
|
102 |
97 101
|
oveq12d |
|
103 |
2 29 32
|
sqdivd |
|
104 |
|
sq2 |
|
105 |
104
|
oveq2i |
|
106 |
103 105
|
eqtrdi |
|
107 |
102 106
|
oveq12d |
|
108 |
96 107
|
eqtr2d |
|
109 |
108 5
|
oveq12d |
|
110 |
89 90 18 6
|
divsubdird |
|
111 |
88 13 18 6
|
div23d |
|
112 |
18
|
sqvald |
|
113 |
112
|
oveq1d |
|
114 |
18 18 6
|
divcan3d |
|
115 |
113 114
|
eqtrd |
|
116 |
115
|
oveq1d |
|
117 |
111 116
|
eqtrd |
|
118 |
18 3 2
|
mul32d |
|
119 |
18 2 3
|
mulassd |
|
120 |
118 119
|
eqtrd |
|
121 |
120
|
oveq1d |
|
122 |
2 3
|
mulcld |
|
123 |
122 18 6
|
divcan3d |
|
124 |
121 123
|
eqtrd |
|
125 |
117 124
|
oveq12d |
|
126 |
110 125
|
eqtrd |
|
127 |
126
|
oveq1d |
|
128 |
93 18 6
|
divcld |
|
129 |
43 122 128
|
subsubd |
|
130 |
127 129
|
eqtr4d |
|
131 |
94 109 130
|
3eqtr3d |
|
132 |
83 87 131
|
3eqtrd |
|
133 |
51 132
|
oveq12d |
|
134 |
48 49
|
addcld |
|
135 |
122 128
|
subcld |
|
136 |
43 134 135
|
pnncand |
|
137 |
128
|
negcld |
|
138 |
48 49 122 137
|
add4d |
|
139 |
122 128
|
negsubd |
|
140 |
139
|
oveq2d |
|
141 |
49 128
|
negsubd |
|
142 |
1 2 3 4 5 6 7 8 9 10
|
dquartlem2 |
|
143 |
141 142
|
eqtrd |
|
144 |
143
|
oveq2d |
|
145 |
48 122 9
|
addassd |
|
146 |
144 145
|
eqtrd |
|
147 |
138 140 146
|
3eqtr3d |
|
148 |
133 136 147
|
3eqtrd |
|
149 |
13 20
|
addcld |
|
150 |
59 4 67
|
divcld |
|
151 |
|
subsq |
|
152 |
149 150 151
|
syl2anc |
|
153 |
148 152
|
eqtr3d |
|
154 |
153
|
eqeq1d |
|
155 |
149 150
|
addcld |
|
156 |
149 150
|
subcld |
|
157 |
155 156
|
mul0ord |
|
158 |
1 2 3 4 5 6 7 8
|
dquartlem1 |
|
159 |
4
|
negcld |
|
160 |
|
sqneg |
|
161 |
16 160
|
syl |
|
162 |
5 161
|
eqtr4d |
|
163 |
|
mulneg2 |
|
164 |
14 4 163
|
sylancr |
|
165 |
164
|
oveq1d |
|
166 |
162 165
|
eqtr4d |
|
167 |
4
|
sqcld |
|
168 |
167
|
negcld |
|
169 |
1
|
halfcld |
|
170 |
168 169
|
subcld |
|
171 |
58 4 67
|
divcld |
|
172 |
170 171
|
negsubd |
|
173 |
|
sqneg |
|
174 |
4 173
|
syl |
|
175 |
174
|
eqcomd |
|
176 |
175
|
negeqd |
|
177 |
176
|
oveq1d |
|
178 |
58 4 67
|
divneg2d |
|
179 |
177 178
|
oveq12d |
|
180 |
12 172 179
|
3eqtr2d |
|
181 |
1 2 3 159 166 6 11 180
|
dquartlem1 |
|
182 |
59 4 67
|
divneg2d |
|
183 |
182
|
oveq2d |
|
184 |
149 150
|
negsubd |
|
185 |
183 184
|
eqtr3d |
|
186 |
185
|
eqeq1d |
|
187 |
4
|
negnegd |
|
188 |
187
|
oveq1d |
|
189 |
188
|
eqeq2d |
|
190 |
187
|
oveq1d |
|
191 |
190
|
eqeq2d |
|
192 |
189 191
|
orbi12d |
|
193 |
181 186 192
|
3bitr3d |
|
194 |
158 193
|
orbi12d |
|
195 |
154 157 194
|
3bitrd |
|