Theorems · Theorem · linear algebra

Module.Basis.finiteDimensional_of_finite

∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {ι : Type w}
  [Finite ι] (h : Module.Basis ι K V), FiniteDimensional K V

If a vector space has a finite basis, then it is finite-dimensional.

Defined in

Mathlib.LinearAlgebra.FiniteDimensional.Defs

Cited by

21 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DivisionRingAddCommGroupModuleFinite