Theorems · Theorem · nonassociative algebras
LieSubmodule.disjoint_toSubmodule
∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [inst_4 : LieRingModule L M] {N N' : LieSubmodule R L M}, Disjoint ↑N ↑N' ↔ Disjoint N N'- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- Disjointstatement and proof · cited by 2,201
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieSubmodule.toSubmodulestatement and proof · cited by 150
- disjoint_iffproof · cited by 76
- LieSubmodule.toSubmodule_injproof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- LieAlgebra.InvariantForm.orthogonal_isCompl_toSubmoduleproof · cited by 3
- LieModule.disjoint_genWeightSpaceOfproof · cited by 1
- LieIdeal.isCompl_killingComplproof · cited by 0