Theorems · Theorem · nonassociative algebras

LieSubmodule.mem_iInf

∀ {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] {ι : Sort u_1} (p : ι → LieSubmodule R L M) {x : M},
  x ∈ ⨅ i, p i ↔ ∀ (i : ι), x ∈ p i

Defined in: Mathlib.Algebra.Lie.Submodule
Cited by: 1 results in Mathlib
Foundations: Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing LieRing AddCommGroup Module LieRingModule

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Cites11

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

Setproof · cited by 53,352
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
iInfstatement · cited by 1,690
LieRingstatement and proof · cited by 1,548
LieRingModulestatement and proof · cited by 727
LieSubmodulestatement and proof · cited by 489
SetLike.mem_coeproof · cited by 302
Set.mem_iInterproof · cited by 69
LieSubmodule.coe_iInfproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

LieAlgebra.lie_mem_genWeightSpace_of_mem_genWeightSpaceproof · cited by 3