Theorems · Theorem · nonassociative algebras
LieModule.IsFaithful.injective_toEnd
∀ {R : Type u} {L : Type v} {M : Type w} {inst : CommRing R} {inst_1 : LieRing L} {inst_2 : LieAlgebra R L}
{inst_3 : AddCommGroup M} {inst_4 : Module R M} {inst_5 : LieRingModule L M} {inst_6 : LieModule R L M}
[self : LieModule.IsFaithful R L M], Function.Injective ⇑(LieModule.toEnd R L M)- Defined in
- Mathlib.Algebra.Lie.OfAssociative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Quot.sound
- Assumes
- LieModule.IsFaithful
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- Module.Endstatement · cited by 774
- LieRingModulestatement and proof · cited by 727
- LieModulestatement and proof · cited by 424
- LieHomstatement · cited by 382
- LieRing.ofAssociativeRingstatement · cited by 227
- LieModule.toEndstatement · cited by 144
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.toEnd_eq_iffproof · cited by 2