Definition df-bj-onehalf

Description: Define the temporary real "one-half". Once the machinery is developed, the real number "one-half" is commonly denoted by ( 1 / 2 ) . (Contributed by BJ, 4-Feb-2023) (New usage is discouraged.)

TODO:

$p |- 1/2 e. R. $= ? $. ( riotacl )

$p |- -. 0R = 1/2 $= ? $. (since -. ( 0R +R 0R ) = 1R )

$p |- 0R

$p |- 1/2

$p |- ( {R `0R ) = 0R $= ? $.

$p |- ( {R1/2 ) = 1/2 $= ? $.

df-minfty $a |- minfty = ( inftyexpitau` <. 1/2 , 0R >. ) $.

	Ref	Expression
Assertion	df-bj-onehalf	⊢ 1/2 = ( ℩ 𝑥 ∈ R ( 𝑥 +R 𝑥 ) = 1R )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		chalf	⊢ 1/2
1		vx	⊢ 𝑥
2		cnr	⊢ R
3	1	cv	⊢ 𝑥
4		cplr	⊢ +R
5	3 3 4	co	⊢ ( 𝑥 +R 𝑥 )
6		c1r	⊢ 1R
7	5 6	wceq	⊢ ( 𝑥 +R 𝑥 ) = 1R
8	7 1 2	crio	⊢ ( ℩ 𝑥 ∈ R ( 𝑥 +R 𝑥 ) = 1R )
9	0 8	wceq	⊢ 1/2 = ( ℩ 𝑥 ∈ R ( 𝑥 +R 𝑥 ) = 1R )