Step |
Hyp |
Ref |
Expression |
1 |
|
chordthmlem5.A |
|
2 |
|
chordthmlem5.B |
|
3 |
|
chordthmlem5.Q |
|
4 |
|
chordthmlem5.X |
|
5 |
|
chordthmlem5.P |
|
6 |
|
chordthmlem5.ABequidistQ |
|
7 |
1 2
|
addcld |
|
8 |
7
|
halfcld |
|
9 |
3 8
|
subcld |
|
10 |
9
|
abscld |
|
11 |
10
|
recnd |
|
12 |
11
|
sqcld |
|
13 |
2 8
|
subcld |
|
14 |
13
|
abscld |
|
15 |
14
|
recnd |
|
16 |
15
|
sqcld |
|
17 |
|
unitssre |
|
18 |
17 4
|
sselid |
|
19 |
18
|
recnd |
|
20 |
19 1
|
mulcld |
|
21 |
|
1cnd |
|
22 |
21 19
|
subcld |
|
23 |
22 2
|
mulcld |
|
24 |
20 23
|
addcld |
|
25 |
5 24
|
eqeltrd |
|
26 |
25 8
|
subcld |
|
27 |
26
|
abscld |
|
28 |
27
|
recnd |
|
29 |
28
|
sqcld |
|
30 |
12 16 29
|
pnpcand |
|
31 |
|
0red |
|
32 |
|
eqidd |
|
33 |
1
|
mul02d |
|
34 |
21
|
subid1d |
|
35 |
34
|
oveq1d |
|
36 |
2
|
mulid2d |
|
37 |
35 36
|
eqtrd |
|
38 |
33 37
|
oveq12d |
|
39 |
2
|
addid2d |
|
40 |
38 39
|
eqtr2d |
|
41 |
1 2 3 31 32 40 6
|
chordthmlem3 |
|
42 |
1 2 3 18 32 5 6
|
chordthmlem3 |
|
43 |
41 42
|
oveq12d |
|
44 |
1 2 4 32 5
|
chordthmlem4 |
|
45 |
30 43 44
|
3eqtr4rd |
|