Step | Hyp | Ref
| Expression |
1 | | quart.a |
. . . 4
|
2 | | quart.b |
. . . 4
|
3 | | quart.c |
. . . 4
|
4 | | quart.d |
. . . 4
|
5 | | quart.p |
. . . 4
|
6 | | quart.q |
. . . 4
|
7 | | quart.r |
. . . 4
; ;; |
8 | | quart.x |
. . . 4
|
9 | | quart.e |
. . . . . 6
|
10 | 9 | oveq2d 6666 |
. . . . 5
|
11 | | 4cn 11098 |
. . . . . . . 8
|
12 | 11 | a1i 11 |
. . . . . . 7
|
13 | | 4ne0 11117 |
. . . . . . . 8
|
14 | 13 | a1i 11 |
. . . . . . 7
|
15 | 1, 12, 14 | divcld 10801 |
. . . . . 6
|
16 | 8, 15 | subnegd 10399 |
. . . . 5
|
17 | 10, 16 | eqtrd 2656 |
. . . 4
|
18 | 1, 2, 3, 4, 5, 6, 7, 8, 17 | quart1 24583 |
. . 3
|
19 | 18 | eqeq1d 2624 |
. 2
|
20 | 1, 2, 3, 4, 5, 6, 7 | quart1cl 24581 |
. . . 4
|
21 | 20 | simp1d 1073 |
. . 3
|
22 | 20 | simp2d 1074 |
. . 3
|
23 | 15 | negcld 10379 |
. . . . 5
|
24 | 9, 23 | eqeltrd 2701 |
. . . 4
|
25 | 8, 24 | subcld 10392 |
. . 3
|
26 | | quart.u |
. . . . 5
; |
27 | | quart.v |
. . . . 5
; ;
|
28 | | quart.w |
. . . . 5
|
29 | | quart.s |
. . . . 5
|
30 | | quart.m |
. . . . 5
|
31 | | quart.t |
. . . . 5
|
32 | | quart.t0 |
. . . . 5
|
33 | 1, 2, 3, 4, 1, 9, 5, 6, 7, 26,
27, 28, 29, 30, 31, 32 | quartlem3 24586 |
. . . 4
|
34 | 33 | simp1d 1073 |
. . 3
|
35 | 29 | oveq2d 6666 |
. . . . . 6
|
36 | 33 | simp2d 1074 |
. . . . . . . 8
|
37 | 36 | sqrtcld 14176 |
. . . . . . 7
|
38 | | 2cnd 11093 |
. . . . . . 7
|
39 | | 2ne0 11113 |
. . . . . . . 8
|
40 | 39 | a1i 11 |
. . . . . . 7
|
41 | 37, 38, 40 | divcan2d 10803 |
. . . . . 6
|
42 | 35, 41 | eqtrd 2656 |
. . . . 5
|
43 | 42 | oveq1d 6665 |
. . . 4
|
44 | 36 | sqsqrtd 14178 |
. . . 4
|
45 | 43, 44 | eqtr2d 2657 |
. . 3
|
46 | | quart.m0 |
. . 3
|
47 | | quart.i |
. . . . 5
|
48 | | quart.j |
. . . . 5
|
49 | 1, 2, 3, 4, 1, 9, 5, 6, 7, 26,
27, 28, 29, 30, 31, 32, 46, 47, 48 | quartlem4 24587 |
. . . 4
|
50 | 49 | simp2d 1074 |
. . 3
|
51 | 47 | oveq1d 6665 |
. . . 4
|
52 | 34 | sqcld 13006 |
. . . . . . . 8
|
53 | 52 | negcld 10379 |
. . . . . . 7
|
54 | 21 | halfcld 11277 |
. . . . . . 7
|
55 | 53, 54 | subcld 10392 |
. . . . . 6
|
56 | 22, 12, 14 | divcld 10801 |
. . . . . . 7
|
57 | 49 | simp1d 1073 |
. . . . . . 7
|
58 | 56, 34, 57 | divcld 10801 |
. . . . . 6
|
59 | 55, 58 | addcld 10059 |
. . . . 5
|
60 | 59 | sqsqrtd 14178 |
. . . 4
|
61 | 51, 60 | eqtrd 2656 |
. . 3
|
62 | 20 | simp3d 1075 |
. . 3
|
63 | | 1cnd 10056 |
. . . . 5
|
64 | | 3z 11410 |
. . . . . 6
|
65 | | 1exp 12889 |
. . . . . 6
|
66 | 64, 65 | mp1i 13 |
. . . . 5
|
67 | 33 | simp3d 1075 |
. . . . . . . . . . 11
|
68 | 67 | mulid2d 10058 |
. . . . . . . . . 10
|
69 | 68 | oveq2d 6666 |
. . . . . . . . 9
|
70 | 68 | oveq2d 6666 |
. . . . . . . . 9
|
71 | 69, 70 | oveq12d 6668 |
. . . . . . . 8
|
72 | 71 | oveq1d 6665 |
. . . . . . 7
|
73 | 72 | negeqd 10275 |
. . . . . 6
|
74 | 30, 73 | eqtr4d 2659 |
. . . . 5
|
75 | | oveq1 6657 |
. . . . . . . 8
|
76 | 75 | eqeq1d 2624 |
. . . . . . 7
|
77 | | oveq1 6657 |
. . . . . . . . . . . 12
|
78 | 77 | oveq2d 6666 |
. . . . . . . . . . 11
|
79 | 77 | oveq2d 6666 |
. . . . . . . . . . 11
|
80 | 78, 79 | oveq12d 6668 |
. . . . . . . . . 10
|
81 | 80 | oveq1d 6665 |
. . . . . . . . 9
|
82 | 81 | negeqd 10275 |
. . . . . . . 8
|
83 | 82 | eqeq2d 2632 |
. . . . . . 7
|
84 | 76, 83 | anbi12d 747 |
. . . . . 6
|
85 | 84 | rspcev 3309 |
. . . . 5
|
86 | 63, 66, 74, 85 | syl12anc 1324 |
. . . 4
|
87 | | 2cn 11091 |
. . . . . 6
|
88 | | mulcl 10020 |
. . . . . 6
|
89 | 87, 21, 88 | sylancr 695 |
. . . . 5
|
90 | 21 | sqcld 13006 |
. . . . . 6
|
91 | | mulcl 10020 |
. . . . . . 7
|
92 | 11, 62, 91 | sylancr 695 |
. . . . . 6
|
93 | 90, 92 | subcld 10392 |
. . . . 5
|
94 | 22 | sqcld 13006 |
. . . . . 6
|
95 | 94 | negcld 10379 |
. . . . 5
|
96 | 31 | oveq1d 6665 |
. . . . . 6
|
97 | 1, 2, 3, 4, 1, 9, 5, 6, 7, 26,
27, 28 | quartlem2 24585 |
. . . . . . . . . 10
|
98 | 97 | simp2d 1074 |
. . . . . . . . 9
|
99 | 97 | simp3d 1075 |
. . . . . . . . 9
|
100 | 98, 99 | addcld 10059 |
. . . . . . . 8
|
101 | 100 | halfcld 11277 |
. . . . . . 7
|
102 | | 3nn 11186 |
. . . . . . 7
|
103 | | cxproot 24436 |
. . . . . . 7
|
104 | 101, 102,
103 | sylancl 694 |
. . . . . 6
|
105 | 96, 104 | eqtrd 2656 |
. . . . 5
|
106 | 28 | oveq1d 6665 |
. . . . . 6
|
107 | 98 | sqcld 13006 |
. . . . . . . 8
|
108 | 97 | simp1d 1073 |
. . . . . . . . . 10
|
109 | | 3nn0 11310 |
. . . . . . . . . 10
|
110 | | expcl 12878 |
. . . . . . . . . 10
|
111 | 108, 109,
110 | sylancl 694 |
. . . . . . . . 9
|
112 | | mulcl 10020 |
. . . . . . . . 9
|
113 | 11, 111, 112 | sylancr 695 |
. . . . . . . 8
|
114 | 107, 113 | subcld 10392 |
. . . . . . 7
|
115 | 114 | sqsqrtd 14178 |
. . . . . 6
|
116 | 106, 115 | eqtrd 2656 |
. . . . 5
|
117 | 21, 22, 62, 26, 27 | quartlem1 24584 |
. . . . . 6
; |
118 | 117 | simpld 475 |
. . . . 5
|
119 | 117 | simprd 479 |
. . . . 5
; |
120 | 89, 93, 95, 36, 67, 105, 99, 116, 118, 119, 32 | mcubic 24574 |
. . . 4
|
121 | 86, 120 | mpbird 247 |
. . 3
|
122 | 49 | simp3d 1075 |
. . 3
|
123 | 48 | oveq1d 6665 |
. . . 4
|
124 | 55, 58 | subcld 10392 |
. . . . 5
|
125 | 124 | sqsqrtd 14178 |
. . . 4
|
126 | 123, 125 | eqtrd 2656 |
. . 3
|
127 | 21, 22, 25, 34, 45, 46, 50, 61, 62, 121, 122, 126 | dquart 24580 |
. 2
|
128 | 34 | negcld 10379 |
. . . . . . . 8
|
129 | 128, 50 | addcld 10059 |
. . . . . . 7
|
130 | 8, 24, 129 | subaddd 10410 |
. . . . . 6
|
131 | 24, 34 | negsubd 10398 |
. . . . . . . . 9
|
132 | 131 | oveq1d 6665 |
. . . . . . . 8
|
133 | 24, 128, 50 | addassd 10062 |
. . . . . . . 8
|
134 | 132, 133 | eqtr3d 2658 |
. . . . . . 7
|
135 | 134 | eqeq1d 2624 |
. . . . . 6
|
136 | 130, 135 | bitr4d 271 |
. . . . 5
|
137 | | eqcom 2629 |
. . . . 5
|
138 | 136, 137 | syl6bb 276 |
. . . 4
|
139 | 128, 50 | subcld 10392 |
. . . . . . 7
|
140 | 8, 24, 139 | subaddd 10410 |
. . . . . 6
|
141 | 131 | oveq1d 6665 |
. . . . . . . 8
|
142 | 24, 128, 50 | addsubassd 10412 |
. . . . . . . 8
|
143 | 141, 142 | eqtr3d 2658 |
. . . . . . 7
|
144 | 143 | eqeq1d 2624 |
. . . . . 6
|
145 | 140, 144 | bitr4d 271 |
. . . . 5
|
146 | | eqcom 2629 |
. . . . 5
|
147 | 145, 146 | syl6bb 276 |
. . . 4
|
148 | 138, 147 | orbi12d 746 |
. . 3
|
149 | 34, 122 | addcld 10059 |
. . . . . . 7
|
150 | 8, 24, 149 | subaddd 10410 |
. . . . . 6
|
151 | 24, 34, 122 | addassd 10062 |
. . . . . . 7
|
152 | 151 | eqeq1d 2624 |
. . . . . 6
|
153 | 150, 152 | bitr4d 271 |
. . . . 5
|
154 | | eqcom 2629 |
. . . . 5
|
155 | 153, 154 | syl6bb 276 |
. . . 4
|
156 | 34, 122 | subcld 10392 |
. . . . . . 7
|
157 | 8, 24, 156 | subaddd 10410 |
. . . . . 6
|
158 | 24, 34, 122 | addsubassd 10412 |
. . . . . . 7
|
159 | 158 | eqeq1d 2624 |
. . . . . 6
|
160 | 157, 159 | bitr4d 271 |
. . . . 5
|
161 | | eqcom 2629 |
. . . . 5
|
162 | 160, 161 | syl6bb 276 |
. . . 4
|
163 | 155, 162 | orbi12d 746 |
. . 3
|
164 | 148, 163 | orbi12d 746 |
. 2
|
165 | 19, 127, 164 | 3bitrd 294 |
1
|