Theorems · Theorem · nonassociative algebras
LieSubalgebra.coe_toLieSubmodule
∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (K : LieSubalgebra R L),
↑K.toLieSubmodule = K.toSubmodule- Defined in
- Mathlib.Algebra.Lie.Submodule
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
- 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
- LieSubalgebrastatement and proof · cited by 418
- LieSubmodule.toSubmodulestatement · cited by 150
- LieSubalgebra.toSubmodulestatement · cited by 90
- LieSubalgebra.toLieSubmodulestatement · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- LieAlgebra.rootSpace_zero_eqproof · cited by 9
- LieAlgebra.le_zeroRootSubalgebraproof · cited by 3
- LieSubalgebra.normalizer_eq_self_of_isCartanSubalgebraproof · cited by 3
- LieSubalgebra.normalizer_eq_self_iffproof · cited by 1
- LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebraproof · cited by 1
- LieSubalgebra.isCartanSubalgebra_iff_isUcsLimitproof · cited by 0