Switch maps (and consequently most of the code) to using instances

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>

Lattice.agda

@@ -187,8 +187,8 @@ record IsLattice {a} (A : Set a)
     (_⊓_ : A → A → A) : Set a where
 
     field
-        joinSemilattice : IsSemilattice A _≈_ _⊔_
-        meetSemilattice : IsSemilattice A _≈_ _⊓_
+        {{joinSemilattice}} : IsSemilattice A _≈_ _⊔_
+        {{meetSemilattice}} : IsSemilattice A _≈_ _⊓_
 
         absorb-⊔-⊓ : (x y : A) → (x ⊔ (x ⊓ y)) ≈ x
         absorb-⊓-⊔ : (x y : A) → (x ⊓ (x ⊔ y)) ≈ x
@@ -217,12 +217,12 @@ record IsFiniteHeightLattice {a} (A : Set a)
     (_⊓_ : A → A → A) : Set (lsuc a) where
 
     field
-        isLattice : IsLattice A _≈_ _⊔_ _⊓_
+        {{isLattice}} : IsLattice A _≈_ _⊔_ _⊓_
 
     open IsLattice isLattice public
 
     field
-        fixedHeight : FixedHeight h
+        {{fixedHeight}} : FixedHeight h
 
 module ChainMapping {a b} {A : Set a} {B : Set b}
     {_≈₁_ : A → A → Set a} {_≈₂_ : B → B → Set b}
@@ -252,7 +252,7 @@ record Semilattice {a} (A : Set a) : Set (lsuc a) where
         _≈_ : A → A → Set a
         _⊔_ : A → A → A
 
-        isSemilattice : IsSemilattice A _≈_ _⊔_
+        {{isSemilattice}} : IsSemilattice A _≈_ _⊔_
 
     open IsSemilattice isSemilattice public
 
@@ -263,7 +263,7 @@ record Lattice {a} (A : Set a) : Set (lsuc a) where
         _⊔_ : A → A → A
         _⊓_ : A → A → A
 
-        isLattice : IsLattice A _≈_ _⊔_ _⊓_
+        {{isLattice}} : IsLattice A _≈_ _⊔_ _⊓_
 
     open IsLattice isLattice public
 
@@ -274,6 +274,6 @@ record FiniteHeightLattice {a} (A : Set a) : Set (lsuc a) where
         _⊔_ : A → A → A
         _⊓_ : A → A → A
 
-        isFiniteHeightLattice : IsFiniteHeightLattice A height _≈_ _⊔_ _⊓_
+        {{isFiniteHeightLattice}} : IsFiniteHeightLattice A height _≈_ _⊔_ _⊓_
 
     open IsFiniteHeightLattice isFiniteHeightLattice public