feat: root space decomposition of ideals of Lie algebras

[jano-wol]

Root space decomposition of ideals of Lie algebras

PR proves that in an IsKilling Lie algebra, every Lie ideal decomposes as its intersection with the Cartan subalgebra plus a sum of root spaces. This result is needed for two larger proofs:

1. Showing the order isomorphism between Lie ideals and invariant root submodules.
2. Showing that semisimple Lie algebras with irreducible root system are simple.

[github-actions]

PR summary eb5df47f87

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ instIsTriangularizableLieIdeal
+ isAtom_of_finrank_eq_one
+ lieIdeal_eq_iSup_inf_genWeightSpace
+ lieIdeal_eq_inf_cartan_sup_biSup_inf_rootSpace
+ lieIdeal_eq_inf_cartan_sup_biSup_rootSpace

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 scripts/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).

[ocfnash]

I'm not convinced by this lemma. It's really a statement about atoms of lattices and submodules of rank 1. I think the result about atoms is already covered since we have things like:

example {α : Type*} [CompleteLattice α] (a b : α) (ha : IsAtom a) :
    a ≤ b ∨ Disjoint a b := by
  rw [← ha.not_le_iff_disjoint]
  tauto

but after a quick look I seem not to be able to find the result that a submodule of finrank 1 is an atom (over a field). So that might be worth adding if you need it to use the lemmas about IsAtom as above.

[jano-wol]

I decommissioned rootSpace_le_or_disjoint and added a lemma on finrank 1 -> IsAtom. Please check, I hope it is good now!