Theorems · Theorem · linear algebra

Submodule.mem_dualCoannihilator

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  {Φ : Submodule R (Module.Dual R M)} (x : M), x ∈ Φ.dualCoannihilator ↔ ∀ φ ∈ Φ, φ x = 0

Defined in

Mathlib.LinearAlgebra.Dual.Defs

Cited by

2 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringAddCommMonoidModule