[Merged by Bors] - feat: injectivity of Function.extend for disjoint ranges

[kim-em]

This PR adds Function.Injective.extend_of_disjoint: if f : α → β, g : α → γ and j : β → γ are injective and g and j have disjoint ranges, then Function.extend f g j is injective. It is used in leanprover/cslib#401 to build families of total orders for a comparison-sorting lower bound, via Function.extend f Sum.inl Sum.inr : β → α ⊕ β.

🤖 Prepared with Claude Code

[github-actions]

PR summary f8c3dba6af

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ _root_.Function.Injective.extend_of_disjoint

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 f8c3dba).

• +1 new declarations
• −0 removed declarations

+Function.Injective.extend_of_disjoint

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No changes to strong technical debt.
No changes to weak technical debt.

Current commit f8c3dba6af
Reference commit 1318ddb253

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.py 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).

[eric-wieser]

Gemini suggests the more general result

theorem Injective.extend_of_disjoint {α β γ : Type*} 
    {f : α → β} {g : α → γ} {h : β → γ}
    (hf : Injective f) (hg : Injective g) (hh : Injective h)
    (hd : Disjoint (range g) (range h)) :
    Injective (extend f g h) := by

[kim-em]

Done.

[eric-wieser]

nit: I think we have a lemma that directly proves injectivity.

Given that, i'd suggest just dropping this specialization entirely.

bors d+

[mathlib-bors]

✌️ kim-em can now approve this pull request until 2026-09-23 05:34 UTC (in 2 weeks). To approve and merge, reply with bors r+. More detailed instructions are available here.

⚠️ This delegation only covers changes within Archive/**, Counterexamples/**, docs/**, DownstreamTest/**, Mathlib/**, MathlibTest/**, Wanted/**, widget/**, Archive.lean, Counterexamples.lean, docs.lean, Mathlib.lean, Wanted.lean; an author commit touching anything else will revoke it. Bors also revokes it if a later push changes too many files for it to check the full list — even if it stays within scope.

[kim-em]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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