Theorems · Definition · linear algebra

Module.Basis.indexEquiv

{R : Type u} →
  {M : Type v} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {ι : Type w} → {ι' : Type w'} → [InvariantBasisNumber R] → Module.Basis ι R M → Module.Basis ι' R M → ι ≃ ι'

Given two bases indexed by ι and ι' of an R-module, where R satisfies the invariant basis number property, an equiv ι ≃ ι'.

Defined in

Mathlib.LinearAlgebra.Dimension.StrongRankCondition

Cited by

9 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleInvariantBasisNumber