Move equiv rels (#46)

Sets/EquivalenceRelations.agda

@@ -0,0 +1,23 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+open import LogicalFormulae
+open import Functions
+
+module Sets.EquivalenceRelations where
+
+Reflexive : {a b : _} {A : Set a} (r : Rel {a} {b} A) → Set (a ⊔ b)
+Reflexive {A = A} r = {x : A} → r x x
+
+Symmetric : {a b : _} {A : Set a} (r : Rel {a} {b} A) → Set (a ⊔ b)
+Symmetric {A = A} r = {x y : A} → r x y → r y x
+
+Transitive : {a b : _} {A : Set a} (r : Rel {a} {b} A) → Set (a ⊔ b)
+Transitive {A = A} r = {x y z : A} → r x y → r y z → r x z
+
+record Equivalence {a b : _} {A : Set a} (r : Rel {a} {b} A) : Set (a ⊔ lsuc b) where
+  field
+    reflexive : Reflexive r
+    symmetric : Symmetric r
+    transitive : Transitive r