Step |
Hyp |
Ref |
Expression |
1 |
|
nnrp |
|
2 |
1
|
ad2antrr |
|
3 |
|
1rp |
|
4 |
3
|
a1i |
|
5 |
2 4
|
rpaddcld |
|
6 |
5
|
rpsqrtcld |
|
7 |
6
|
rpred |
|
8 |
2
|
rpsqrtcld |
|
9 |
8
|
rpred |
|
10 |
|
nn0re |
|
11 |
10
|
adantr |
|
12 |
11
|
ad2antlr |
|
13 |
|
nn0re |
|
14 |
13
|
adantl |
|
15 |
14
|
ad2antlr |
|
16 |
9 15
|
remulcld |
|
17 |
2
|
rpred |
|
18 |
|
1re |
|
19 |
18
|
a1i |
|
20 |
15
|
resqcld |
|
21 |
19 20
|
resubcld |
|
22 |
17 21
|
remulcld |
|
23 |
|
0red |
|
24 |
17 23
|
remulcld |
|
25 |
12
|
resqcld |
|
26 |
|
sq1 |
|
27 |
26
|
a1i |
|
28 |
|
nnge1 |
|
29 |
28
|
adantl |
|
30 |
|
simplrl |
|
31 |
|
oveq1 |
|
32 |
31
|
adantl |
|
33 |
|
sq0 |
|
34 |
32 33
|
eqtrdi |
|
35 |
34
|
oveq2d |
|
36 |
2
|
rpcnd |
|
37 |
36
|
adantr |
|
38 |
37
|
mul01d |
|
39 |
35 38
|
eqtrd |
|
40 |
39
|
oveq2d |
|
41 |
|
simplrr |
|
42 |
12
|
recnd |
|
43 |
42
|
sqcld |
|
44 |
43
|
adantr |
|
45 |
44
|
subid1d |
|
46 |
40 41 45
|
3eqtr3d |
|
47 |
26 46
|
eqtr2id |
|
48 |
|
nn0ge0 |
|
49 |
48
|
adantr |
|
50 |
49
|
ad2antlr |
|
51 |
|
0le1 |
|
52 |
51
|
a1i |
|
53 |
|
sq11 |
|
54 |
12 50 19 52 53
|
syl22anc |
|
55 |
54
|
adantr |
|
56 |
47 55
|
mpbid |
|
57 |
|
simpr |
|
58 |
57
|
oveq2d |
|
59 |
8
|
rpcnd |
|
60 |
59
|
adantr |
|
61 |
60
|
mul01d |
|
62 |
58 61
|
eqtrd |
|
63 |
56 62
|
oveq12d |
|
64 |
|
1p0e1 |
|
65 |
63 64
|
eqtrdi |
|
66 |
30 65
|
breqtrd |
|
67 |
18
|
ltnri |
|
68 |
|
pm2.24 |
|
69 |
66 67 68
|
mpisyl |
|
70 |
|
simplrr |
|
71 |
|
elnn0 |
|
72 |
70 71
|
sylib |
|
73 |
29 69 72
|
mpjaodan |
|
74 |
|
nn0ge0 |
|
75 |
74
|
adantl |
|
76 |
75
|
ad2antlr |
|
77 |
19 15 52 76
|
le2sqd |
|
78 |
73 77
|
mpbid |
|
79 |
27 78
|
eqbrtrrd |
|
80 |
19 20
|
suble0d |
|
81 |
79 80
|
mpbird |
|
82 |
21 23 2
|
lemul2d |
|
83 |
81 82
|
mpbid |
|
84 |
22 24 25 83
|
leadd2dd |
|
85 |
5
|
rpcnd |
|
86 |
85
|
sqsqrtd |
|
87 |
|
simprr |
|
88 |
87
|
eqcomd |
|
89 |
88
|
oveq2d |
|
90 |
15
|
recnd |
|
91 |
90
|
sqcld |
|
92 |
36 91
|
mulcld |
|
93 |
36 43 92
|
addsub12d |
|
94 |
19
|
recnd |
|
95 |
36 94 91
|
subdid |
|
96 |
36
|
mulid1d |
|
97 |
96
|
oveq1d |
|
98 |
95 97
|
eqtr2d |
|
99 |
98
|
oveq2d |
|
100 |
93 99
|
eqtrd |
|
101 |
86 89 100
|
3eqtrd |
|
102 |
36
|
mul01d |
|
103 |
102
|
oveq2d |
|
104 |
43
|
addid1d |
|
105 |
103 104
|
eqtr2d |
|
106 |
84 101 105
|
3brtr4d |
|
107 |
6
|
rpge0d |
|
108 |
7 12 107 50
|
le2sqd |
|
109 |
106 108
|
mpbird |
|
110 |
59
|
mulid1d |
|
111 |
19 15 8
|
lemul2d |
|
112 |
73 111
|
mpbid |
|
113 |
110 112
|
eqbrtrrd |
|
114 |
7 9 12 16 109 113
|
le2addd |
|