Step |
Hyp |
Ref |
Expression |
1 |
|
quart.a |
|
2 |
|
quart.b |
|
3 |
|
quart.c |
|
4 |
|
quart.d |
|
5 |
|
quart.x |
|
6 |
|
quart.e |
|
7 |
|
quart.p |
|
8 |
|
quart.q |
|
9 |
|
quart.r |
|
10 |
|
quart.u |
|
11 |
|
quart.v |
|
12 |
|
quart.w |
|
13 |
|
quart.s |
|
14 |
|
quart.m |
|
15 |
|
quart.t |
|
16 |
|
quart.t0 |
|
17 |
|
quart.m0 |
|
18 |
|
quart.i |
|
19 |
|
quart.j |
|
20 |
6
|
oveq2d |
|
21 |
|
4cn |
|
22 |
21
|
a1i |
|
23 |
|
4ne0 |
|
24 |
23
|
a1i |
|
25 |
1 22 24
|
divcld |
|
26 |
5 25
|
subnegd |
|
27 |
20 26
|
eqtrd |
|
28 |
1 2 3 4 7 8 9 5 27
|
quart1 |
|
29 |
28
|
eqeq1d |
|
30 |
1 2 3 4 7 8 9
|
quart1cl |
|
31 |
30
|
simp1d |
|
32 |
30
|
simp2d |
|
33 |
25
|
negcld |
|
34 |
6 33
|
eqeltrd |
|
35 |
5 34
|
subcld |
|
36 |
1 2 3 4 1 6 7 8 9 10 11 12 13 14 15 16
|
quartlem3 |
|
37 |
36
|
simp1d |
|
38 |
13
|
oveq2d |
|
39 |
36
|
simp2d |
|
40 |
39
|
sqrtcld |
|
41 |
|
2cnd |
|
42 |
|
2ne0 |
|
43 |
42
|
a1i |
|
44 |
40 41 43
|
divcan2d |
|
45 |
38 44
|
eqtrd |
|
46 |
45
|
oveq1d |
|
47 |
39
|
sqsqrtd |
|
48 |
46 47
|
eqtr2d |
|
49 |
1 2 3 4 1 6 7 8 9 10 11 12 13 14 15 16 17 18 19
|
quartlem4 |
|
50 |
49
|
simp2d |
|
51 |
18
|
oveq1d |
|
52 |
37
|
sqcld |
|
53 |
52
|
negcld |
|
54 |
31
|
halfcld |
|
55 |
53 54
|
subcld |
|
56 |
32 22 24
|
divcld |
|
57 |
49
|
simp1d |
|
58 |
56 37 57
|
divcld |
|
59 |
55 58
|
addcld |
|
60 |
59
|
sqsqrtd |
|
61 |
51 60
|
eqtrd |
|
62 |
30
|
simp3d |
|
63 |
|
1cnd |
|
64 |
|
3z |
|
65 |
|
1exp |
|
66 |
64 65
|
mp1i |
|
67 |
36
|
simp3d |
|
68 |
67
|
mulid2d |
|
69 |
68
|
oveq2d |
|
70 |
68
|
oveq2d |
|
71 |
69 70
|
oveq12d |
|
72 |
71
|
oveq1d |
|
73 |
72
|
negeqd |
|
74 |
14 73
|
eqtr4d |
|
75 |
|
oveq1 |
|
76 |
75
|
eqeq1d |
|
77 |
|
oveq1 |
|
78 |
77
|
oveq2d |
|
79 |
77
|
oveq2d |
|
80 |
78 79
|
oveq12d |
|
81 |
80
|
oveq1d |
|
82 |
81
|
negeqd |
|
83 |
82
|
eqeq2d |
|
84 |
76 83
|
anbi12d |
|
85 |
84
|
rspcev |
|
86 |
63 66 74 85
|
syl12anc |
|
87 |
|
2cn |
|
88 |
|
mulcl |
|
89 |
87 31 88
|
sylancr |
|
90 |
31
|
sqcld |
|
91 |
|
mulcl |
|
92 |
21 62 91
|
sylancr |
|
93 |
90 92
|
subcld |
|
94 |
32
|
sqcld |
|
95 |
94
|
negcld |
|
96 |
15
|
oveq1d |
|
97 |
1 2 3 4 1 6 7 8 9 10 11 12
|
quartlem2 |
|
98 |
97
|
simp2d |
|
99 |
97
|
simp3d |
|
100 |
98 99
|
addcld |
|
101 |
100
|
halfcld |
|
102 |
|
3nn |
|
103 |
|
cxproot |
|
104 |
101 102 103
|
sylancl |
|
105 |
96 104
|
eqtrd |
|
106 |
12
|
oveq1d |
|
107 |
98
|
sqcld |
|
108 |
97
|
simp1d |
|
109 |
|
3nn0 |
|
110 |
|
expcl |
|
111 |
108 109 110
|
sylancl |
|
112 |
|
mulcl |
|
113 |
21 111 112
|
sylancr |
|
114 |
107 113
|
subcld |
|
115 |
114
|
sqsqrtd |
|
116 |
106 115
|
eqtrd |
|
117 |
31 32 62 10 11
|
quartlem1 |
|
118 |
117
|
simpld |
|
119 |
117
|
simprd |
|
120 |
89 93 95 39 67 105 99 116 118 119 16
|
mcubic |
|
121 |
86 120
|
mpbird |
|
122 |
49
|
simp3d |
|
123 |
19
|
oveq1d |
|
124 |
55 58
|
subcld |
|
125 |
124
|
sqsqrtd |
|
126 |
123 125
|
eqtrd |
|
127 |
31 32 35 37 48 17 50 61 62 121 122 126
|
dquart |
|
128 |
37
|
negcld |
|
129 |
128 50
|
addcld |
|
130 |
5 34 129
|
subaddd |
|
131 |
34 37
|
negsubd |
|
132 |
131
|
oveq1d |
|
133 |
34 128 50
|
addassd |
|
134 |
132 133
|
eqtr3d |
|
135 |
134
|
eqeq1d |
|
136 |
130 135
|
bitr4d |
|
137 |
|
eqcom |
|
138 |
136 137
|
bitrdi |
|
139 |
128 50
|
subcld |
|
140 |
5 34 139
|
subaddd |
|
141 |
131
|
oveq1d |
|
142 |
34 128 50
|
addsubassd |
|
143 |
141 142
|
eqtr3d |
|
144 |
143
|
eqeq1d |
|
145 |
140 144
|
bitr4d |
|
146 |
|
eqcom |
|
147 |
145 146
|
bitrdi |
|
148 |
138 147
|
orbi12d |
|
149 |
37 122
|
addcld |
|
150 |
5 34 149
|
subaddd |
|
151 |
34 37 122
|
addassd |
|
152 |
151
|
eqeq1d |
|
153 |
150 152
|
bitr4d |
|
154 |
|
eqcom |
|
155 |
153 154
|
bitrdi |
|
156 |
37 122
|
subcld |
|
157 |
5 34 156
|
subaddd |
|
158 |
34 37 122
|
addsubassd |
|
159 |
158
|
eqeq1d |
|
160 |
157 159
|
bitr4d |
|
161 |
|
eqcom |
|
162 |
160 161
|
bitrdi |
|
163 |
155 162
|
orbi12d |
|
164 |
148 163
|
orbi12d |
|
165 |
29 127 164
|
3bitrd |
|