Lots of speedups (#116)

Groups/Orders/Partial/Definition.agda

@@ -0,0 +1,17 @@
+{-# OPTIONS --safe --warning=error --without-K #-}
+
+open import Groups.Definition
+open import Setoids.Orders.Partial.Definition
+open import Setoids.Setoids
+open import Functions
+
+open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
+
+module Groups.Orders.Partial.Definition {n m : _} {A : Set n} {S : Setoid {n} {m} A} {_+_ : A → A → A} (G : Group S _+_) where
+
+open Group G
+open Setoid S
+
+record PartiallyOrderedGroup {p : _} {_<_ : Rel {_} {p} A} (pOrder : SetoidPartialOrder S _<_) : Set (lsuc n ⊔ m ⊔ p) where
+  field
+    orderRespectsAddition : {a b : A} → (a < b) → (c : A) → (a + c) < (b + c)