Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-inftyexpi | Structured version Visualization version GIF version |
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 33100. 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.) |
Ref | Expression |
---|---|
df-bj-inftyexpi | ⊢ inftyexpi = (𝑥 ∈ (-π(,]π) ↦ 〈𝑥, ℂ〉) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cinftyexpi 33093 | . 2 class inftyexpi | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cpi 14797 | . . . . 5 class π | |
4 | 3 | cneg 10267 | . . . 4 class -π |
5 | cioc 12176 | . . . 4 class (,] | |
6 | 4, 3, 5 | co 6650 | . . 3 class (-π(,]π) |
7 | 2 | cv 1482 | . . . 4 class 𝑥 |
8 | cc 9934 | . . . 4 class ℂ | |
9 | 7, 8 | cop 4183 | . . 3 class 〈𝑥, ℂ〉 |
10 | 2, 6, 9 | cmpt 4729 | . 2 class (𝑥 ∈ (-π(,]π) ↦ 〈𝑥, ℂ〉) |
11 | 1, 10 | wceq 1483 | 1 wff inftyexpi = (𝑥 ∈ (-π(,]π) ↦ 〈𝑥, ℂ〉) |
Colors of variables: wff setvar class |
This definition is referenced by: bj-inftyexpiinv 33095 bj-inftyexpidisj 33097 bj-ccinftydisj 33100 bj-elccinfty 33101 bj-minftyccb 33112 |
Copyright terms: Public domain | W3C validator |