Cleanup finset and modulo (#92)

Sets/Cardinality/Countable/Definition.agda

@@ -0,0 +1,27 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+open import LogicalFormulae
+open import Functions
+open import Numbers.Naturals.Semiring
+open import Numbers.Naturals.Order
+open import Numbers.Naturals.Order.Lemmas
+open import Sets.Cardinality.Finite.Definition
+open import Semirings.Definition
+open import Sets.CantorBijection.CantorBijection
+open import Orders.Total.Definition
+
+module Sets.Cardinality.Countable.Definition where
+
+open import Semirings.Lemmas ℕSemiring
+
+record CountablyInfiniteSet {a : _} (A : Set a) : Set a where
+  field
+    counting : A → ℕ
+    countingIsBij : Bijection counting
+
+data Countable {a : _} (A : Set a) : Set a where
+  finite : FiniteSet A → Countable A
+  infinite : CountablyInfiniteSet A → Countable A
+