feat(Topology): generalise IsometricSmul to WeakPseudoEMetricSpace and friends

[felixpernegger]

By Codex GPT 5.6 Sol, reviewed by me

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• depends on: feat(Topology): generalise Isometry to WeakPseudoEMetricSpace and friends #42741

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[github-actions]

PR summary 95dbb5a98c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ instance (priority := 100) IsIsometricSMul.opposite_of_comm [SMul M E] [SMul Mᵐᵒᵖ E]
+ instance (priority := 100) IsIsometricSMul.to_continuousConstSMul [SMul M P]
+ instance : EquivLike (X ≃ᵢ Y) X Y
+ instance : Group (X ≃ᵢ X)
+ instance : IsIsometricSMul M Wᵐᵒᵖ
+ instance : IsometryClass (IsometryEquiv X Y) X Y
+ instance {ι} {X : ι → Type*} [Fintype ι] [∀ i, SMul M (X i)] [∀ i, EDist (X i)]
++-- zero_iff
+-+- preimage_closedEBall
+-+- preimage_eball
+-+-+- edist_eq
- instance (priority := 100) IsIsometricSMul.opposite_of_comm [PseudoEMetricSpace X] [SMul M X]
- instance (priority := 100) IsIsometricSMul.to_continuousConstSMul [PseudoEMetricSpace X] [SMul M X]
- instance : EquivLike (α ≃ᵢ β) α β
- instance : Group (α ≃ᵢ α)
- instance : IsIsometricSMul M Xᵐᵒᵖ
- instance : IsometryClass (IsometryEquiv α β) α β
- instance {ι} {X : ι → Type*} [Fintype ι] [∀ i, SMul M (X i)] [∀ i, PseudoEMetricSpace (X i)]
-++- comp
-++- injective
-+-+ ediam_image
-+-+ ediam_range
-+-+-+ prodMk
-+--+++-+- continuous
--++ comp_continuousOn_iff
--++ comp_continuous_iff
--++ isUniformInducing
--++ prodMk_left
--++ prodMk_right
--++ uniformContinuous

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.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 95dbb5a).

• +0 new declarations
• −0 removed declarations

No declaration differences.

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Increase in strong tech debt: (relative, absolute) = (1.00, 0.04)

Current number	Change	Type (strong)
25	1	disabled simpNF lints

No changes to weak technical debt.

Current commit 95dbb5a98c
Reference commit caa4dbde35

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(Topology): generalise Isometry to WeakPseudoEMetricSpace and friends #42741
  By Dependent Issues (🤖). Happy coding!

[felixpernegger]

i think this is a false positive, as the suggested simp makes no progress

[felixpernegger]

LLM-generated