Step |
Hyp |
Ref |
Expression |
1 |
|
2cn |
|
2 |
|
simpll |
|
3 |
|
simprl |
|
4 |
|
remulcl |
|
5 |
2 3 4
|
syl2anc |
|
6 |
|
mulge0 |
|
7 |
|
resqrtcl |
|
8 |
5 6 7
|
syl2anc |
|
9 |
8
|
recnd |
|
10 |
|
sqmul |
|
11 |
1 9 10
|
sylancr |
|
12 |
|
sq2 |
|
13 |
12
|
oveq1i |
|
14 |
5
|
recnd |
|
15 |
|
sqrtth |
|
16 |
14 15
|
syl |
|
17 |
16
|
oveq2d |
|
18 |
13 17
|
syl5eq |
|
19 |
11 18
|
eqtrd |
|
20 |
2 3
|
resubcld |
|
21 |
20
|
sqge0d |
|
22 |
2
|
recnd |
|
23 |
3
|
recnd |
|
24 |
|
binom2 |
|
25 |
22 23 24
|
syl2anc |
|
26 |
|
binom2sub |
|
27 |
22 23 26
|
syl2anc |
|
28 |
25 27
|
oveq12d |
|
29 |
2
|
resqcld |
|
30 |
|
2re |
|
31 |
|
remulcl |
|
32 |
30 5 31
|
sylancr |
|
33 |
29 32
|
readdcld |
|
34 |
33
|
recnd |
|
35 |
29 32
|
resubcld |
|
36 |
35
|
recnd |
|
37 |
3
|
resqcld |
|
38 |
37
|
recnd |
|
39 |
34 36 38
|
pnpcan2d |
|
40 |
32
|
recnd |
|
41 |
40
|
2timesd |
|
42 |
|
2t2e4 |
|
43 |
42
|
oveq1i |
|
44 |
|
2cnd |
|
45 |
44 44 14
|
mulassd |
|
46 |
43 45
|
syl5eqr |
|
47 |
29
|
recnd |
|
48 |
47 40 40
|
pnncand |
|
49 |
41 46 48
|
3eqtr4rd |
|
50 |
28 39 49
|
3eqtrd |
|
51 |
2 3
|
readdcld |
|
52 |
51
|
resqcld |
|
53 |
52
|
recnd |
|
54 |
20
|
resqcld |
|
55 |
54
|
recnd |
|
56 |
|
4re |
|
57 |
|
remulcl |
|
58 |
56 5 57
|
sylancr |
|
59 |
58
|
recnd |
|
60 |
|
subsub23 |
|
61 |
53 55 59 60
|
syl3anc |
|
62 |
50 61
|
mpbid |
|
63 |
21 62
|
breqtrrd |
|
64 |
52 58
|
subge0d |
|
65 |
63 64
|
mpbid |
|
66 |
19 65
|
eqbrtrd |
|
67 |
|
remulcl |
|
68 |
30 8 67
|
sylancr |
|
69 |
|
sqrtge0 |
|
70 |
5 6 69
|
syl2anc |
|
71 |
|
0le2 |
|
72 |
|
mulge0 |
|
73 |
30 71 72
|
mpanl12 |
|
74 |
8 70 73
|
syl2anc |
|
75 |
|
addge0 |
|
76 |
75
|
an4s |
|
77 |
68 51 74 76
|
le2sqd |
|
78 |
66 77
|
mpbird |
|
79 |
|
2rp |
|
80 |
79
|
a1i |
|
81 |
8 51 80
|
lemuldiv2d |
|
82 |
78 81
|
mpbid |
|