[Merged by Bors] - feat: define the sl₂ Lie subalgebra associated to a root

[ocfnash]

The lemma root_mem_submodule_iff_of_add_mem_invtSubmodule is related in the sense that it can be used to prove the subalgebra associated to the roots in an invariant submodule is an ideal.

---

[github-actions]

PR summary 3c23e6ba60

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ coroot_neg
+ mem_sl2SubalgebraOfRoot_iff
+ mem_span_triple
+ mem_toLieSubalgebra_iff
+ root_mem_submodule_iff_of_add_mem_invtSubmodule
+ sl2SubalgebraOfRoot
+ toLieSubalgebra
- _root_.LieAlgebra.IsKilling.coroot_neg

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[jcommelin]

Thanks 🎉

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• Build
• Lint style