Theorems · Theorem · nonassociative algebras
LieEquiv.injective
∀ {R : Type u} {L₁ : Type v} {L₂ : Type w} [inst : CommRing R] [inst_1 : LieRing L₁] [inst_2 : LieRing L₂]
[inst_3 : LieAlgebra R L₁] [inst_4 : LieAlgebra R L₂] (e : L₁ ≃ₗ⁅R⁆ L₂), Function.Injective ⇑e.toLieHom- Defined in
- Mathlib.Algebra.Lie.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieHomstatement · cited by 382
- LinearEquiv.injectiveproof · cited by 162
- LieEquivstatement and proof · cited by 86
- LieEquiv.toLinearEquivproof · cited by 16
- LieEquiv.toLieHomstatement · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- LieEquiv.nilpotent_iff_equiv_nilpotentproof · cited by 1
- LieAlgebra.solvable_iff_equiv_solvableproof · cited by 1
- lie_abelian_iff_equiv_lie_abelianproof · cited by 0