Move Bool to live on its own (#118)

Groups/Definition.agda

@@ -1,5 +1,6 @@
 {-# OPTIONS --safe --warning=error --without-K #-}
 
+open import Sets.EquivalenceRelations
 open import Setoids.Setoids
 open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
 
@@ -16,3 +17,9 @@ record Group {lvl1 lvl2} {A : Set lvl1} (S : Setoid {lvl1} {lvl2} A) (_·_ : A
     identLeft : {a : A} → (0G · a) ∼ a
     invLeft : {a : A} → (inverse a) · a ∼ 0G
     invRight : {a : A} → a · (inverse a) ∼ 0G
+  +Associative' : {a b c : A} → ((a · b) · c) ∼ (a · (b · c))
+  +Associative' = Equivalence.symmetric (Setoid.eq S) +Associative
+  +WellDefinedLeft : {m x n : A} → (m ∼ n) → (m · x) ∼ (n · x)
+  +WellDefinedLeft m=n = +WellDefined m=n (Equivalence.reflexive (Setoid.eq S))
+  +WellDefinedRight : {m x y : A} → (x ∼ y) → (m · x) ∼ (m · y)
+  +WellDefinedRight x=y = +WellDefined (Equivalence.reflexive (Setoid.eq S)) x=y

Groups/FreeGroup/Definition.agda

@@ -10,6 +10,7 @@ open import Sets.FinSet.Definition
 open import Groups.Definition
 open import Groups.SymmetricGroups.Definition
 open import Decidable.Sets
+open import Boolean.Definition
 
 module Groups.FreeGroup.Definition where
 

Groups/FreeGroup/Parity.agda

@@ -11,6 +11,7 @@ open import LogicalFormulae
 open import Semirings.Definition
 open import Functions
 open import Groups.Isomorphisms.Definition
+open import Boolean.Definition
 
 module Groups.FreeGroup.Parity {a : _} {A : Set a} (decA : DecidableSet A) where
 

Groups/FreeGroup/Word.agda

@@ -7,6 +7,7 @@ open import Decidable.Sets
 open import Numbers.Naturals.Semiring
 open import Numbers.Naturals.Order
 open import LogicalFormulae
+open import Boolean.Definition
 
 module Groups.FreeGroup.Word {a : _} {A : Set a} (decA : DecidableSet A) where