Metamath Proof Explorer


Theorem goldrarp

Description: The golden ratio is a positive real. (Contributed by Ender Ting, 16-Apr-2026)

Ref Expression
Hypothesis goldra.val
|- F = ( 2 x. ( cos ` ( _pi / 5 ) ) )
Assertion goldrarp
|- F e. RR+

Proof

Step Hyp Ref Expression
1 goldra.val
 |-  F = ( 2 x. ( cos ` ( _pi / 5 ) ) )
2 1 goldrarr
 |-  F e. RR
3 1 goldrapos
 |-  0 < F
4 2 3 elrpii
 |-  F e. RR+