[Merged by Bors] - feat(RingTheory/MvPowerSeries/Trunc): generalize truncation lemmas

[justus-springer]

Generalize coeff_trunc_mul_trunc_eq_coeff_mul (and its analogs for truncFinset and trunc') to allow for different truncation levels for the two arguments. This matches the API for univariate power series, where we already have PowerSeries.coeff_mul_eq_coeff_trunc_mul_trunc₂.

This is useful for defining partial derivatives of multivariate power series, see PR #39626.

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[github-actions]

PR summary f084f1bbe9

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)

+ coeff_trunc'_mul_trunc'_eq_coeff_mul₂
+ coeff_truncFinset_mul_truncFinset_eq_coeff_mul₂
+ coeff_trunc_mul_trunc_eq_coeff_mul
+ coeff_trunc_mul_trunc_eq_coeff_mul₂

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 f084f1b).

• +4 new declarations
• −0 removed declarations

+MvPowerSeries.coeff_trunc'_mul_trunc'_eq_coeff_mul₂
+MvPowerSeries.coeff_truncFinset_mul_truncFinset_eq_coeff_mul₂
+MvPowerSeries.coeff_trunc_mul_trunc_eq_coeff_mul
+MvPowerSeries.coeff_trunc_mul_trunc_eq_coeff_mul₂

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit f084f1bbe9
Reference commit 8f49886e72

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).

[faenuccio]

@justus-springer Can you update master here as well? Thanks

[tb65536]

Very nice, thanks!

maintainer delegate

[github-actions]

🚀 Pull request has been placed on the maintainer queue by tb65536.

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

✌️ justus-springer can now approve this pull request until 2026-07-10 11:37 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/**, widget/**, Archive.lean, Counterexamples.lean, docs.lean, Mathlib.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.

[justus-springer]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-CI job
• ci (staging) / Post-Build Step
• ci (staging) / Build
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