Step |
Hyp |
Ref |
Expression |
1 |
|
quartlem1.p |
|
2 |
|
quartlem1.q |
|
3 |
|
quartlem1.r |
|
4 |
|
quartlem1.u |
|
5 |
|
quartlem1.v |
|
6 |
|
2cn |
|
7 |
|
sqmul |
|
8 |
6 1 7
|
sylancr |
|
9 |
|
sq2 |
|
10 |
9
|
oveq1i |
|
11 |
8 10
|
eqtrdi |
|
12 |
11
|
oveq1d |
|
13 |
|
4cn |
|
14 |
13
|
a1i |
|
15 |
|
3cn |
|
16 |
15
|
a1i |
|
17 |
1
|
sqcld |
|
18 |
14 16 17
|
subdird |
|
19 |
12 18
|
eqtr4d |
|
20 |
|
ax-1cn |
|
21 |
|
3p1e4 |
|
22 |
13 15 20 21
|
subaddrii |
|
23 |
22
|
oveq1i |
|
24 |
|
mulid2 |
|
25 |
23 24
|
syl5eq |
|
26 |
17 25
|
syl |
|
27 |
19 26
|
eqtr2d |
|
28 |
27
|
oveq1d |
|
29 |
|
mulcl |
|
30 |
6 1 29
|
sylancr |
|
31 |
30
|
sqcld |
|
32 |
|
mulcl |
|
33 |
15 17 32
|
sylancr |
|
34 |
|
1nn0 |
|
35 |
|
2nn |
|
36 |
34 35
|
decnncl |
|
37 |
36
|
nncni |
|
38 |
|
mulcl |
|
39 |
37 3 38
|
sylancr |
|
40 |
31 33 39
|
subsubd |
|
41 |
28 40
|
eqtr4d |
|
42 |
|
mulcl |
|
43 |
13 3 42
|
sylancr |
|
44 |
16 17 43
|
subdid |
|
45 |
|
4t3e12 |
|
46 |
13 15 45
|
mulcomli |
|
47 |
46
|
oveq1i |
|
48 |
16 14 3
|
mulassd |
|
49 |
47 48
|
eqtr3id |
|
50 |
49
|
oveq2d |
|
51 |
44 50
|
eqtr4d |
|
52 |
51
|
oveq2d |
|
53 |
41 4 52
|
3eqtr4d |
|
54 |
6
|
a1i |
|
55 |
|
3nn0 |
|
56 |
55
|
a1i |
|
57 |
54 1 56
|
mulexpd |
|
58 |
|
cu2 |
|
59 |
58
|
oveq1i |
|
60 |
57 59
|
eqtrdi |
|
61 |
60
|
oveq2d |
|
62 |
|
8cn |
|
63 |
62
|
a1i |
|
64 |
|
expcl |
|
65 |
1 55 64
|
sylancl |
|
66 |
54 63 65
|
mul12d |
|
67 |
61 66
|
eqtrd |
|
68 |
|
9cn |
|
69 |
68
|
a1i |
|
70 |
|
mulcl |
|
71 |
6 65 70
|
sylancr |
|
72 |
1 3
|
mulcld |
|
73 |
|
mulcl |
|
74 |
62 72 73
|
sylancr |
|
75 |
69 71 74
|
subdid |
|
76 |
30 17 43
|
subdid |
|
77 |
54 1 17
|
mulassd |
|
78 |
1 17
|
mulcomd |
|
79 |
|
df-3 |
|
80 |
79
|
oveq2i |
|
81 |
|
2nn0 |
|
82 |
|
expp1 |
|
83 |
1 81 82
|
sylancl |
|
84 |
80 83
|
syl5eq |
|
85 |
78 84
|
eqtr4d |
|
86 |
85
|
oveq2d |
|
87 |
77 86
|
eqtrd |
|
88 |
54 1 14 3
|
mul4d |
|
89 |
|
4t2e8 |
|
90 |
13 6 89
|
mulcomli |
|
91 |
90
|
oveq1i |
|
92 |
88 91
|
eqtrdi |
|
93 |
87 92
|
oveq12d |
|
94 |
76 93
|
eqtrd |
|
95 |
94
|
oveq2d |
|
96 |
|
9t8e72 |
|
97 |
96
|
oveq1i |
|
98 |
69 63 72
|
mulassd |
|
99 |
97 98
|
eqtr3id |
|
100 |
99
|
oveq2d |
|
101 |
75 95 100
|
3eqtr4d |
|
102 |
67 101
|
oveq12d |
|
103 |
|
mulcl |
|
104 |
62 71 103
|
sylancr |
|
105 |
|
mulcl |
|
106 |
68 71 105
|
sylancr |
|
107 |
|
7nn0 |
|
108 |
107 35
|
decnncl |
|
109 |
108
|
nncni |
|
110 |
|
mulcl |
|
111 |
109 72 110
|
sylancr |
|
112 |
104 106 111
|
subsubd |
|
113 |
106 104
|
negsubdi2d |
|
114 |
69 63 71
|
subdird |
|
115 |
|
8p1e9 |
|
116 |
68 62 20 115
|
subaddrii |
|
117 |
116
|
oveq1i |
|
118 |
71
|
mulid2d |
|
119 |
117 118
|
syl5eq |
|
120 |
114 119
|
eqtr3d |
|
121 |
120
|
negeqd |
|
122 |
113 121
|
eqtr3d |
|
123 |
122
|
oveq1d |
|
124 |
102 112 123
|
3eqtrd |
|
125 |
|
7nn |
|
126 |
81 125
|
decnncl |
|
127 |
126
|
nncni |
|
128 |
2
|
sqcld |
|
129 |
|
mulneg2 |
|
130 |
127 128 129
|
sylancr |
|
131 |
124 130
|
oveq12d |
|
132 |
71
|
negcld |
|
133 |
|
mulcl |
|
134 |
127 128 133
|
sylancr |
|
135 |
132 111 134
|
addsubd |
|
136 |
132 111
|
addcld |
|
137 |
136 134
|
negsubd |
|
138 |
135 137 5
|
3eqtr4d |
|
139 |
131 138
|
eqtr2d |
|
140 |
53 139
|
jca |
|