Theorems · Theorem · nonassociative algebras
LieSubmodule.ext
∀ {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), (∀ (m : M), m ∈ N ↔ m ∈ N') → N = N'- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- LieRingstatement and proof · cited by 1,548
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- SetLike.extproof · cited by 92
Cited by20
Results whose statement or proof uses this declaration.
- LieModuleHom.map_topproof · cited by 6
- LieHom.idealRange_eq_mapproof · cited by 4
- LieIdeal.ker_inclproof · cited by 3
- LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_supproof · cited by 3
- LieAlgebra.self_module_ker_eq_centerproof · cited by 3
- LieDerivation.ad_ker_eq_centerproof · cited by 3
- LieModule.nontrivial_of_isIrreducibleproof · cited by 2
- LieIdeal.idealizer_eq_normalizerproof · cited by 2
- LieSubmodule.comap_normalizerproof · cited by 1
- LieSubmodule.ext_iffproof · cited by 1
- LieAlgebra.isKilling_of_equivproof · cited by 1
- LieModule.isTrivial_iff_max_triv_eq_topproof · cited by 1