feat: lemmas showing properties of ofDerivation added

[Ljon4ik4]

Given an R-Lie algebra L and a commutative R-algebra A, there is a Lie algebra structure on (A ⊗[R] L).
A derivation of A induces a Lie derivation of (A ⊗[R] L), and one obtains a Lie algebra map

ofDerivation : Derivation R A A →ₗ⁅R⁆ LieDerivation R (A ⊗[R] L) (A ⊗[R] L)

In this PR we add a Lemma showing that ofDerivation is in fact A-linear, and that the resulting LieDerivation satisfies a Leibniz rule with respect to the A-multiplication on A ⊗[R] L.

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[github-actions]

PR summary 015537dbab

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)

+ ofDerivation_leibniz
+ ofDerivation_smul

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 015537d).

• +2 new declarations
• −0 removed declarations

+Lie.Derivation.ofDerivation_leibniz
+Lie.Derivation.ofDerivation_smul

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 015537dbab
Reference commit c81c5cbb1c

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).