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Definition df-bj-inftyexpi 32271
 Description: Definition of the auxiliary function inftyexpi parameterizing the circle at infinity ℂ∞ in ℂ̅. We use coupling with ℂ to simplify the proof of bj-ccinftydisj 32277. It could seem more natural to define inftyexpi on all of ℝ using prcpal but we want to use only basic functions in the definition of ℂ̅. (Contributed by BJ, 22-Jun-2019.) The precise definition is irrelevant and should generally not be used. (New usage is discouraged.)
Assertion
Ref Expression
df-bj-inftyexpi inftyexpi = (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)

Detailed syntax breakdown of Definition df-bj-inftyexpi
StepHypRef Expression
1 cinftyexpi 32270 . 2 class inftyexpi
2 vx . . 3 setvar 𝑥
3 cpi 14636 . . . . 5 class π
43cneg 10146 . . . 4 class
5 cioc 12047 . . . 4 class (,]
64, 3, 5co 6549 . . 3 class (-π(,]π)
72cv 1474 . . . 4 class 𝑥
8 cc 9813 . . . 4 class
97, 8cop 4131 . . 3 class 𝑥, ℂ⟩
102, 6, 9cmpt 4643 . 2 class (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)
111, 10wceq 1475 1 wff inftyexpi = (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)
 Colors of variables: wff setvar class This definition is referenced by:  bj-inftyexpiinv  32272  bj-inftyexpidisj  32274  bj-ccinftydisj  32277  bj-elccinfty  32278  bj-minftyccb  32289
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