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Theorems · Theorem · nonassociative algebras

LieSubalgebra.smul_mem

∀ {R : Type u} {L : Type v} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] (L' : LieSubalgebra R L)
  (t : R) {x : L}, x ∈ L' → t • x ∈ L'
Defined in
Mathlib.Algebra.Lie.Subalgebra
Cited by
6 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
CommRingLieRingLieAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieSubalgebra.lieSpan_induction · cited by 9LieSubalgebra.lieSpan_ind…IsSl2Triple.h_eq_coroot · cited by 4IsSl2Triple.h_eq_corootLieAlgebra.IsKilling.lie_eq_killingForm_smul_of_mem_rootSpace_of_mem_rootSpace_neg_aux · cited by 2IsKilling.lie_eq_killingF…LieSubalgebra.lie_mem_sup_of_mem_normalizer · cited by 1LieSubalgebra.lie_mem_sup…LieSubalgebra.comap_lieSpan_range_eq · cited by 0LieSubalgebra.comap_lieSp…LieSubalgebra.lieSpan_lieSpan_coe_preimage · cited by 0LieSubalgebra.lieSpan_lie…CommRing · cited by 17173CommRingLieRing · cited by 1548LieRingLieAlgebra · cited by 1246LieAlgebraLieSubalgebra · cited by 418LieSubalgebraSMulMemClass.smul_mem · cited by 55SMulMemClass.smul_memLieSubalgebra.smul_memCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.