Tidy up groups (#64)

Groups/FiniteGroups/Definition.agda

@@ -0,0 +1,20 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import LogicalFormulae
+open import Setoids.Setoids
+open import Functions
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+open import Numbers.Naturals.Naturals
+open import Sets.FinSet
+open import Groups.Definition
+open import Sets.EquivalenceRelations
+
+module Groups.FiniteGroups.Definition where
+
+record FiniteGroup {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_·_ : A → A → A} (G : Group S _·_) {c : _} (quotientSet : Set c) : Set (a ⊔ b ⊔ c) where
+  field
+    toSet : SetoidToSet S quotientSet
+    finite : FiniteSet quotientSet
+
+groupOrder : {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_·_ : A → A → A} {underG : Group S _·_} {c : _} {quotientSet : Set c} (G : FiniteGroup underG quotientSet) → ℕ
+groupOrder record { toSet = toSet ; finite = record { size = size ; mapping = mapping ; bij = bij } } = size