indexEquiv — Mathlib

English

Given two bases v and v' of M, there exists a bijection ι ≃ ι' between their index sets.

Русский

Для двух баз v и v' существует биекция между их индексами.

LaTeX

$$$\exists \phi : ι \to échanges ι',\ \phi \text{ bijective}$ between indices of bases.$$

Lean4

/-- Given two bases indexed by `ι` and `ι'` of an `R`-module, where `R` satisfies the invariant
basis number property, an equiv `ι ≃ ι'`. -/
def indexEquiv (v : Basis ι R M) (v' : Basis ι' R M) : ι ≃ ι' :=
  (Cardinal.lift_mk_eq'.1 <| mk_eq_mk_of_basis v v').some

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