instFintypeOfDecidableEq — Mathlib

English

If α is a simple ordered set with a least and greatest element, then α has a finite structure and is isomorphic to Bool under a decidable equality.

Русский

Если α упорядочено просто с наименьшим и наибольшим элементами, то α конечно и изоморфно Bool при разрешимой эквивалентности.

LaTeX

$$$\\text{IsSimpleOrder } α \\Rightarrow (\\#α = 2) \\text{ under decidable equality}$$$

Lean4

/-- It is important that `IsSimpleOrder` is the last type-class argument of this instance,
so that type-class inference fails quickly if it doesn't apply.

Note that as of 2025-08-13, this is false. Could someone investigate? -/
scoped instance (priority := 200) [DecidableEq α] : Fintype α :=
  Fintype.ofEquiv Bool equivBool.symm

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