Free-group lemmas (#106)

Setoids/Cardinality/Finite/Definition.agda

@@ -0,0 +1,16 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import Functions
+open import Numbers.Naturals.Definition
+open import Sets.FinSet.Definition
+open import Setoids.Setoids
+
+module Setoids.Cardinality.Finite.Definition where
+
+record FiniteSetoid {a b : _} {A : Set a} (S : Setoid {a} {b} A) : Set (a ⊔ b) where
+  field
+    size : ℕ
+    mapping : FinSet size → A
+    bij : SetoidBijection (reflSetoid (FinSet size)) S mapping
+