Metamath Proof Explorer


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 = ( iota_ x e. 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
 |-  ( iota_ x e. R. ( x +R x ) = 1R )
9 0 8 wceq
 |-  1/2 = ( iota_ x e. R. ( x +R x ) = 1R )