chore: complete generalization of oneLePart lemmas to DivInvMonoid

[kim-em]

This PR completes the generalization of Mathlib/Algebra/Order/Group/PosPart.lean started by #41247: weaken leOnePart_one/negPart_zero from Group to DivInvOneMonoid (the proof needs only inv_one), weaken oneLePart_min and the five oneLePart lemmas in the LinearOrder section (oneLePart_eq_ite, oneLePart_eq_ite_lt, one_lt_oneLePart_iff, oneLePart_of_one_lt_oneLePart, oneLePart_lt) from Group to DivInvMonoid, and weaken the Pi section's [∀ i, Group (α i)] to [∀ i, DivInvMonoid (α i)]. No statement or proof changes; this makes these lemmas available for EReal, the motivating use case of the original PR.

Follow-up to #41247 (chore: generalize instPosPart to SubNegMonoid).

🤖 Prepared with Claude Code

[github-actions]

PR summary 2e33d17998

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 (regex)

No declarations were harmed in the making of this PR! 🐙

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 2e33d17).

• +0 new declarations
• −0 removed declarations

No declaration differences.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 2e33d17998
Reference commit a33a5ccd63

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).

[themathqueen]

!radar

[leanprover-radar]

Benchmark results for 2e33d17 against a33a5cc are in. No significant results found. @themathqueen

Warning

These warnings may indicate that the benchmark results are not directly comparable, for example due to changes in the runner configuration or hardware.

• Bench repo commit hashes for run main differ between commits.

• ✅ build//instructions: -171.2G (-0.11%)

Small changes (1✅)

1 hidden