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Theorems · Theorem · nonassociative algebras

LieSubmodule.mem_coe

∀ {R : Type u} {L : Type v} {M : Type w} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : AddCommGroup M]
  [inst_3 : Module R M] [inst_4 : LieRingModule L M] (N : LieSubmodule R L M) {x : M}, x ∈ ↑N ↔ x ∈ N
Defined in
Mathlib.Algebra.Lie.Submodule
Cited by
1 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
CommRingLieRingAddCommGroupModuleLieRingModule
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Around this declaration

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

LieHom.mem_idealRange_iff · cited by 1LieHom.mem_idealRange_iffSet · cited by 53352SetModule · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupSetLike.coe · cited by 8199SetLike.coeLieRing · cited by 1548LieRingLieRingModule · cited by 727LieRingModuleLieSubmodule · cited by 489LieSubmoduleLieSubmodule.mem_coeCITED BYCITES

Cites8

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Cited by1

Results whose statement or proof uses this declaration.