Metamath Proof Explorer


Definition df-bj-inftyexpi

Description: Definition of the auxiliary function inftyexpi parameterizing the circle at infinity CCinfty in CCbar . We use coupling with CC to simplify the proof of bj-ccinftydisj . It could seem more natural to define inftyexpi on all of RR , but we want to use only basic functions in the definition of CCbar . TODO: transition to df-bj-inftyexpitau instead. (Contributed by BJ, 22-Jun-2019) The precise definition is irrelevant and should generally not be used. (New usage is discouraged.)

Ref Expression
Assertion df-bj-inftyexpi
|- inftyexpi = ( x e. ( -u _pi (,] _pi ) |-> <. x , CC >. )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cinftyexpi
 |-  inftyexpi
1 vx
 |-  x
2 cpi
 |-  _pi
3 2 cneg
 |-  -u _pi
4 cioc
 |-  (,]
5 3 2 4 co
 |-  ( -u _pi (,] _pi )
6 1 cv
 |-  x
7 cc
 |-  CC
8 6 7 cop
 |-  <. x , CC >.
9 1 5 8 cmpt
 |-  ( x e. ( -u _pi (,] _pi ) |-> <. x , CC >. )
10 0 9 wceq
 |-  inftyexpi = ( x e. ( -u _pi (,] _pi ) |-> <. x , CC >. )