Theorems · Definition · combinatorics

Fintype.truncEquivOfCardEq

{α : Type u_1} →
  {β : Type u_2} →
    [inst : Fintype α] →
      [inst_1 : Fintype β] → [DecidableEq α] → [DecidableEq β] → Fintype.card α = Fintype.card β → Trunc (α ≃ β)

Two Fintypes with the same cardinality are (computably) in bijection. See Fintype.equivOfCardEq for the noncomputable version, and Fintype.truncEquivFinOfCardEq and Fintype.equivFinOfCardEq for the specialization to Fin.

Defined in

Mathlib.Data.Fintype.EquivFin

Cited by

1 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeFintypeDecidableEqDecidableEq