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feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567

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feat(Mathlib/Data/Finite/Option): option type is finite iff type is finite #39567

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38fe3ed
added finiteness conditions to option type
AlexBrodbelt Apr 22, 2026
53ac572
feat(Mathlib/Data/Finite/Option): option type is finite iff type is f…
AlexBrodbelt May 19, 2026
3ca377b
remove min import command
AlexBrodbelt May 19, 2026
99baf79
add new file to Mathlib.lean
AlexBrodbelt May 19, 2026
a88c8cc
added docstrings and comments to files
AlexBrodbelt May 19, 2026
7531e4e
follow modifications from review
AlexBrodbelt May 19, 2026
a5cd43a
modify imports
AlexBrodbelt May 19, 2026
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1 change: 1 addition & 0 deletions Mathlib.lean
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Expand Up @@ -3820,6 +3820,7 @@ public import Mathlib.Data.FinEnum
public import Mathlib.Data.FinEnum.Option
public import Mathlib.Data.Finite.Card
public import Mathlib.Data.Finite.Defs
public import Mathlib.Data.Finite.Option
public import Mathlib.Data.Finite.Perm
public import Mathlib.Data.Finite.Prod
public import Mathlib.Data.Finite.Set
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24 changes: 24 additions & 0 deletions Mathlib/Data/Finite/Option.lean
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@@ -0,0 +1,24 @@
/-
Copyright (c) 2026 Alex Brodbelt. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Brodbelt, Eric Wieser
-/
module

public import Mathlib.Data.Finite.Defs
import Mathlib.Data.Fintype.Option
import Mathlib.Logic.Equiv.Fin.Basic

/-!
# Finiteness conditions for `Option` types

@themathqueen themathqueen Jun 2, 2026

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Suggested change
# Finiteness conditions for `Option` types
# Finiteness conditions for `Option` types
This file shows that `Option α` is finite iff `α` is.

-/

public section

/-- The `Option` type on a type is finite if and only if the underlying type is finite. -/

@themathqueen themathqueen Jun 2, 2026

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How about just

Suggested change
/-- The `Option` type on a type is finite if and only if the underlying type is finite. -/
/-- `Option α` is finite if and only if the underlying type `α` is finite. -/

@[simp]
theorem Option.finite_iff {α : Type*} : Finite (Option α) ↔ Finite α where
mpr _ := inferInstance
mp
| @Finite.intro _ 0 e => (e none).elim0
| @Finite.intro _ (n + 1) e => ⟨(e.trans (finSuccEquiv n)).removeNone⟩
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