Theorems · Theorem · linear algebra

linearIndependent_le_infinite_basis

∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [StrongRankCondition R]
  {ι : Type w} (b : Module.Basis ι R M) [Infinite ι] {κ : Type w} (v : κ → M),
  LinearIndependent R v → Cardinal.mk κ ≤ Cardinal.mk ι

An auxiliary lemma for linearIndependent_le_basis: we handle the case where the basis b is infinite.

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

1 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleStrongRankConditionInfinite