Step |
Hyp |
Ref |
Expression |
1 |
|
rrndistlt.i |
|
2 |
|
rrndistlt.z |
|
3 |
|
rrndistlt.n |
|
4 |
|
rrndistlt.x |
|
5 |
|
rrndistlt.y |
|
6 |
|
rrndistlt.l |
|
7 |
|
rrndistlt.e |
|
8 |
|
rrndistlt.d |
|
9 |
|
elmapi |
|
10 |
4 9
|
syl |
|
11 |
|
ax-resscn |
|
12 |
11
|
a1i |
|
13 |
10 12
|
fssd |
|
14 |
13
|
ffvelrnda |
|
15 |
|
elmapi |
|
16 |
5 15
|
syl |
|
17 |
16 12
|
fssd |
|
18 |
17
|
ffvelrnda |
|
19 |
14 18
|
subcld |
|
20 |
19
|
abscld |
|
21 |
20
|
resqcld |
|
22 |
7
|
rpred |
|
23 |
22
|
resqcld |
|
24 |
23
|
adantr |
|
25 |
19
|
absge0d |
|
26 |
22
|
adantr |
|
27 |
7
|
adantr |
|
28 |
27
|
rpge0d |
|
29 |
|
lt2sq |
|
30 |
20 25 26 28 29
|
syl22anc |
|
31 |
6 30
|
mpbid |
|
32 |
1 2 21 24 31
|
fsumlt |
|
33 |
10
|
ffvelrnda |
|
34 |
16
|
ffvelrnda |
|
35 |
33 34
|
resubcld |
|
36 |
|
absresq |
|
37 |
35 36
|
syl |
|
38 |
37
|
eqcomd |
|
39 |
38
|
sumeq2dv |
|
40 |
11 23
|
sseldi |
|
41 |
|
fsumconst |
|
42 |
1 40 41
|
syl2anc |
|
43 |
|
eqcom |
|
44 |
3 43
|
mpbi |
|
45 |
44
|
oveq1i |
|
46 |
45
|
a1i |
|
47 |
42 46
|
eqtr2d |
|
48 |
39 47
|
breq12d |
|
49 |
32 48
|
mpbird |
|
50 |
|
nfv |
|
51 |
35
|
resqcld |
|
52 |
50 1 51
|
fsumreclf |
|
53 |
35
|
sqge0d |
|
54 |
1 51 53
|
fsumge0 |
|
55 |
|
hashcl |
|
56 |
1 55
|
syl |
|
57 |
3 56
|
eqeltrid |
|
58 |
57
|
nn0red |
|
59 |
58 23
|
remulcld |
|
60 |
57
|
nn0ge0d |
|
61 |
22
|
sqge0d |
|
62 |
58 23 60 61
|
mulge0d |
|
63 |
52 54 59 62
|
sqrtltd |
|
64 |
49 63
|
mpbid |
|
65 |
8
|
a1i |
|
66 |
|
eqid |
|
67 |
|
eqid |
|
68 |
66 67
|
rrxdsfi |
|
69 |
1 68
|
syl |
|
70 |
65 69
|
eqtrd |
|
71 |
|
fveq1 |
|
72 |
71
|
adantr |
|
73 |
|
fveq1 |
|
74 |
73
|
adantl |
|
75 |
72 74
|
oveq12d |
|
76 |
75
|
oveq1d |
|
77 |
76
|
sumeq2sdv |
|
78 |
77
|
fveq2d |
|
79 |
78
|
adantl |
|
80 |
52 54
|
resqrtcld |
|
81 |
70 79 4 5 80
|
ovmpod |
|
82 |
|
sqrtmul |
|
83 |
58 60 23 61 82
|
syl22anc |
|
84 |
7
|
rpge0d |
|
85 |
22 84
|
sqrtsqd |
|
86 |
85
|
oveq2d |
|
87 |
83 86
|
eqtr2d |
|
88 |
81 87
|
breq12d |
|
89 |
64 88
|
mpbird |
|