feat: a base for the root system of a Lie algebra can be promoted to a basis

[ocfnash]

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[github-actions]

PR summary 6f9c636e99

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Algebra.Lie.Basis.Base	2404	2406	+2 (+0.08%)

Import changes for all files

Files	Import difference
3 files Mathlib.Algebra.Lie.Basis.Base Mathlib.Algebra.Lie.Basis Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basis	2

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Declarations diff (regex)

+ cartan_eq_lieSpan
+ coe_add
+ comap_incl_eq_top
+ exists_basis_of_base
+ exists_mem_rootSpace_lie_ne_zero
+ exists_mem_rootSpace_lie_ne_zero'
+ instance : InvolutiveNeg H.root
+ lieSpan_range_union_eq_top_of_mem_rootSpace
+ neg_root_eq
+ neg_root_eq_reflection
+ toSubmodule_rootSpace_eq_span
+ val_neg_root

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 6f9c636).

• +10 new declarations
• −0 removed declarations

+LieAlgebra.IsKilling.exists_mem_rootSpace_lie_ne_zero
+LieAlgebra.IsKilling.instInvolutiveNegSubtypeWeightMemLieSubalgebraFinsetRoot
+LieAlgebra.IsKilling.neg_root_eq
+LieAlgebra.IsKilling.neg_root_eq_reflection
+LieAlgebra.IsKilling.toSubmodule_rootSpace_eq_span
+LieAlgebra.IsKilling.val_neg_root
+LieAlgebra.exists_basis_of_base
+LieAlgebra.lieSpan_range_union_eq_top_of_mem_rootSpace
+LieSubalgebra.comap_incl_eq_top
+LinearMap.coe_add

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 6f9c636e99
Reference commit 4dfbeb6dfa

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).