chore: define Complex.UnitDisc using Subsemigroup.unitBall

[ocfnash]

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[github-actions]

PR summary dcd756f437

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ Subsemigroup.mem_unitBall
- instCommSemigroup

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.

[ADedecker]

Thanks!

bors merge

[eric-wieser]

bors r-

Can you elaborate in the PR description on the benefit of this? Inferring all the instances as inferInstanceAs <| SemigroupWithZero (ball _ _) except this one which is derived from Subsemigroup.unitBall feels like it will just slow down instance unification.

[mathlib-bors]

Canceled.

Address comments or fix if necessary, and then someone with permission can run bors r+.

[ocfnash]

The motivation is to have some local consistency between the definitions of Circle and Complex.UnitDisc. At the moment, there is a mild style inconsistency since Circle uses Submonoid.unitSphere whereas Complex.UnitDisc uses a raw Metric.ball.

The background is that we are about to add Complex.closedUnitDisc and so the question arose about which pattern to follow. I decided that we should follow Circle and bring Complex.UnitDisc in line.

I admit I did not consider the potential performance point you raise but I would be very surprised if it mattered.

[eric-wieser]

Note that Circle does not use deriving, presumably for the performance reasons I mention:

mathlib4/Mathlib/Analysis/Complex/Circle.lean

Lines 50 to 51 in 54f98fd

	def Circle : Type := Submonoid.unitSphere ℂ
	deriving TopologicalSpace

mathlib4/Mathlib/Analysis/Complex/Circle.lean

Line 58 in 54f98fd

instance instCommGroup : CommGroup Circle := inferInstanceAs <| CommGroup (sphere _ _)