feat: Port/Data.FunLike.Fintype (#1933)

port of data.fun_like.fintype

Mathlib.lean

@@ -329,6 +329,7 @@ import Mathlib.Data.Fintype.Vector
 import Mathlib.Data.FunLike.Basic
 import Mathlib.Data.FunLike.Embedding
 import Mathlib.Data.FunLike.Equiv
+import Mathlib.Data.FunLike.Fintype
 import Mathlib.Data.HashMap
 import Mathlib.Data.Int.AbsoluteValue
 import Mathlib.Data.Int.Associated

Mathlib/Data/FunLike/Fintype.lean

@@ -0,0 +1,82 @@
+/-
+Copyright (c) 2022 Anne Baanen. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+Authors: Anne Baanen
+
+! This file was ported from Lean 3 source module data.fun_like.fintype
+! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
+! Please do not edit these lines, except to modify the commit id
+! if you have ported upstream changes.
+-/
+import Mathlib.Data.Finite.Basic
+import Mathlib.Data.Fintype.Basic
+import Mathlib.Data.FunLike.Basic
+
+/-!
+# Finiteness of `FunLike` types
+
+We show a type `F` with a `FunLike F α β` is finite if both `α` and `β` are finite.
+This corresponds to the following two pairs of declarations:
+
+ * `FunLike.fintype` is a definition stating all `FunLike`s are finite if their domain and
+   codomain are.
+ * `FunLike.finite` is a lemma stating all `FunLike`s are finite if their domain and
+   codomain are.
+ * `FunLike.fintype'` is a non-dependent version of `FunLike.fintype` and
+ * `FunLike.finite` is a non-dependent version of `FunLike.finite`, because dependent instances
+   are harder to infer.
+
+You can use these to produce instances for specific `FunLike` types.
+(Although there might be options for `Fintype` instances with better definitional behaviour.)
+They can't be instances themselves since they can cause loops.
+-/
+
+-- porting notes: `Type` is a reserved word, switched to `Type'`
+section Type'
+
+variable (F G : Type _) {α γ : Type _} {β : α → Type _} [FunLike F α β] [FunLike G α fun _ => γ]
+
+/-- All `FunLike`s are finite if their domain and codomain are.
+
+This is not an instance because specific `FunLike` types might have a better-suited definition.
+
+See also `FunLike.finite`.
+-/
+noncomputable def FunLike.fintype [DecidableEq α] [Fintype α] [∀ i, Fintype (β i)] : Fintype F :=
+  Fintype.ofInjective _ FunLike.coe_injective
+#align fun_like.fintype FunLike.fintype
+
+/-- All `FunLike`s are finite if their domain and codomain are.
+
+Non-dependent version of `FunLike.fintype` that might be easier to infer.
+This is not an instance because specific `FunLike` types might have a better-suited definition.
+-/
+noncomputable def FunLike.fintype' [DecidableEq α] [Fintype α] [Fintype γ] : Fintype G :=
+  FunLike.fintype G
+#align fun_like.fintype' FunLike.fintype'
+
+end Type'
+
+-- porting notes: `Sort` is a reserved word, switched to `Sort'`
+section Sort'
+
+variable (F G : Sort _) {α γ : Sort _} {β : α → Sort _} [FunLike F α β] [FunLike G α fun _ => γ]
+
+/-- All `FunLike`s are finite if their domain and codomain are.
+
+Can't be an instance because it can cause infinite loops.
+-/
+theorem FunLike.finite [Finite α] [∀ i, Finite (β i)] : Finite F :=
+  Finite.of_injective _ FunLike.coe_injective
+#align fun_like.finite FunLike.finite
+
+/-- All `FunLike`s are finite if their domain and codomain are.
+
+Non-dependent version of `FunLike.finite` that might be easier to infer.
+Can't be an instance because it can cause infinite loops.
+-/
+theorem FunLike.finite' [Finite α] [Finite γ] : Finite G :=
+  FunLike.finite G
+#align fun_like.finite' FunLike.finite'
+
+end Sort'