Theorems · Theorem · nonassociative algebras
LieIdeal.toLieSubalgebra_toSubmodule
∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (I : LieIdeal R L), (LieIdeal.toLieSubalgebra R L I).toSubmodule = ↑I
- Defined in
- Mathlib.Algebra.Lie.Ideal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- CommRingLieRingLieAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Submodulestatement · cited by 7,192
- LieRingstatement and proof · cited by 1,548
- LieAlgebrastatement and proof · cited by 1,246
- LieIdealstatement and proof · cited by 282
- LieSubmodule.toSubmodulestatement · cited by 150
- LieSubalgebra.toSubmodulestatement · cited by 90
- LieIdeal.toLieSubalgebrastatement · cited by 48
Cited by5
Results whose statement or proof uses this declaration.
- LieIdeal.incl_idealRangeproof · cited by 3
- LieIdeal.coe_map_of_surjectiveproof · cited by 2
- LieAlgebra.exists_engelian_lieSubalgebra_of_lt_normalizerproof · cited by 1
- LieHom.range_inlproof · cited by 1
- LieHom.range_inrproof · cited by 1