Theorems · Theorem · nonassociative algebras
LieSubmodule.Quotient.mk_eq_zero
∀ {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 : LieSubmodule R L M) [inst_5 : LieAlgebra R L]
[inst_6 : LieModule R L M] {m : M}, (LieSubmodule.Quotient.mk' N) m = 0 ↔ m ∈ N- Defined in
- Mathlib.Algebra.Lie.Quotient
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 95 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.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- HasQuotient.Quotientstatement · cited by 2,301
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieRingModulestatement and proof · cited by 727
- LieSubmodulestatement and proof · cited by 489
- LieModulestatement and proof · cited by 424
- LieSubmodule.toSubmoduleproof · cited by 150
- LieModuleHomstatement · cited by 123
Cited by2
Results whose statement or proof uses this declaration.
- LieAlgebra.engel_isBot_of_isMinproof · cited by 1
- LieSubalgebra.normalizer_eq_self_iffproof · cited by 1