Theorems · Theorem · linear algebra

FiniteDimensional.mem_span_of_iInf_ker_le_ker

∀ {ι : Type u_3} {𝕜 : Type u_4} {E : Type u_5} [inst : Field 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
  [FiniteDimensional 𝕜 E] {L : ι → E →ₗ[𝕜] 𝕜} {K : E →ₗ[𝕜] 𝕜},
  ⨅ i, (L i).ker ≤ K.ker → K ∈ Submodule.span 𝕜 (Set.range L)

Defined in

Mathlib.LinearAlgebra.Dual.Lemmas

Cited by

1 results in Mathlib

Foundations

Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional