Step |
Hyp |
Ref |
Expression |
1 |
|
rmspecnonsq |
|
2 |
|
eluzelz |
|
3 |
|
zsqcl |
|
4 |
2 3
|
syl |
|
5 |
4
|
zred |
|
6 |
|
1red |
|
7 |
5 6
|
resubcld |
|
8 |
|
sq1 |
|
9 |
8
|
a1i |
|
10 |
|
eluz2b2 |
|
11 |
10
|
simprbi |
|
12 |
|
eluzelre |
|
13 |
|
0le1 |
|
14 |
13
|
a1i |
|
15 |
|
eluzge2nn0 |
|
16 |
15
|
nn0ge0d |
|
17 |
6 12 14 16
|
lt2sqd |
|
18 |
11 17
|
mpbid |
|
19 |
9 18
|
eqbrtrrd |
|
20 |
6 5
|
posdifd |
|
21 |
19 20
|
mpbid |
|
22 |
7 21
|
elrpd |
|
23 |
22
|
rpsqrtcld |
|
24 |
23
|
rpred |
|
25 |
24
|
recnd |
|
26 |
25
|
mulid1d |
|
27 |
26
|
oveq2d |
|
28 |
|
pell1qrss14 |
|
29 |
1 28
|
syl |
|
30 |
|
1nn0 |
|
31 |
30
|
a1i |
|
32 |
8
|
oveq2i |
|
33 |
7
|
recnd |
|
34 |
33
|
mulid1d |
|
35 |
32 34
|
eqtrid |
|
36 |
35
|
oveq2d |
|
37 |
5
|
recnd |
|
38 |
|
1cnd |
|
39 |
37 38
|
nncand |
|
40 |
36 39
|
eqtrd |
|
41 |
|
pellqrexplicit |
|
42 |
1 15 31 40 41
|
syl31anc |
|
43 |
29 42
|
sseldd |
|
44 |
27 43
|
eqeltrrd |
|
45 |
6 24
|
readdcld |
|
46 |
12 24
|
readdcld |
|
47 |
6 23
|
ltaddrpd |
|
48 |
6 12 24 11
|
ltadd1dd |
|
49 |
6 45 46 47 48
|
lttrd |
|
50 |
|
pellfundlb |
|
51 |
1 44 49 50
|
syl3anc |
|
52 |
37 38
|
npcand |
|
53 |
52
|
fveq2d |
|
54 |
12 16
|
sqrtsqd |
|
55 |
53 54
|
eqtrd |
|
56 |
55
|
oveq1d |
|
57 |
|
pellfundge |
|
58 |
1 57
|
syl |
|
59 |
56 58
|
eqbrtrrd |
|
60 |
|
pellfundre |
|
61 |
1 60
|
syl |
|
62 |
61 46
|
letri3d |
|
63 |
51 59 62
|
mpbir2and |
|