Theorems · Theorem · linear algebra

Subspace.forall_mem_dualAnnihilator_apply_eq_zero_iff

∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] (W : Subspace K V)
  (v : V), (∀ φ ∈ Submodule.dualAnnihilator W, φ v = 0) ↔ v ∈ W

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

2 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModule