Make 'isLattice' for simple types be an instance

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

Lattice/Nat.agda

@@ -18,31 +18,32 @@ private
     ≡-⊓-cong : ∀ {a₁ a₂ a₃ a₄} → a₁ ≡ a₂ → a₃ ≡ a₄ → (a₁ ⊓ a₃) ≡ (a₂ ⊓ a₄)
     ≡-⊓-cong a₁≡a₂ a₃≡a₄ rewrite a₁≡a₂ rewrite a₃≡a₄ = refl
 
-isMaxSemilattice : IsSemilattice ℕ _≡_ _⊔_
-isMaxSemilattice = record
-    { ≈-equiv = record
-        { ≈-refl = refl
-        ; ≈-sym = sym
-        ; ≈-trans = trans
+instance
+    isMaxSemilattice : IsSemilattice ℕ _≡_ _⊔_
+    isMaxSemilattice = record
+        { ≈-equiv = record
+            { ≈-refl = refl
+            ; ≈-sym = sym
+            ; ≈-trans = trans
+            }
+        ; ≈-⊔-cong = ≡-⊔-cong
+        ; ⊔-assoc = ⊔-assoc
+        ; ⊔-comm = ⊔-comm
+        ; ⊔-idemp = ⊔-idem
         }
-    ; ≈-⊔-cong = ≡-⊔-cong
-    ; ⊔-assoc = ⊔-assoc
-    ; ⊔-comm = ⊔-comm
-    ; ⊔-idemp = ⊔-idem
-    }
 
-isMinSemilattice : IsSemilattice ℕ _≡_ _⊓_
-isMinSemilattice = record
-    { ≈-equiv = record
-        { ≈-refl = refl
-        ; ≈-sym = sym
-        ; ≈-trans = trans
+    isMinSemilattice : IsSemilattice ℕ _≡_ _⊓_
+    isMinSemilattice = record
+        { ≈-equiv = record
+            { ≈-refl = refl
+            ; ≈-sym = sym
+            ; ≈-trans = trans
+            }
+        ; ≈-⊔-cong = ≡-⊓-cong
+        ; ⊔-assoc = ⊓-assoc
+        ; ⊔-comm = ⊓-comm
+        ; ⊔-idemp = ⊓-idem
         }
-    ; ≈-⊔-cong = ≡-⊓-cong
-    ; ⊔-assoc = ⊓-assoc
-    ; ⊔-comm = ⊓-comm
-    ; ⊔-idemp = ⊓-idem
-    }
 
 private
     max-bound₁ : {x y z : ℕ} → x ⊔ y ≡ z → x ≤ z
@@ -74,18 +75,19 @@ private
             helper : x ⊔ (x ⊓ y) ≤ x ⊔ x  → x ⊔ x ≡ x → x ⊔ (x ⊓ y) ≤ x
             helper x⊔x⊓y≤x⊔x x⊔x≡x rewrite x⊔x≡x = x⊔x⊓y≤x⊔x
 
-isLattice : IsLattice ℕ _≡_ _⊔_ _⊓_
-isLattice = record
-    { joinSemilattice = isMaxSemilattice
-    ; meetSemilattice = isMinSemilattice
-    ; absorb-⊔-⊓ = λ x y → maxmin-absorb {x} {y}
-    ; absorb-⊓-⊔ = λ x y → minmax-absorb {x} {y}
-    }
+instance
+    isLattice : IsLattice ℕ _≡_ _⊔_ _⊓_
+    isLattice = record
+        { joinSemilattice = isMaxSemilattice
+        ; meetSemilattice = isMinSemilattice
+        ; absorb-⊔-⊓ = λ x y → maxmin-absorb {x} {y}
+        ; absorb-⊓-⊔ = λ x y → minmax-absorb {x} {y}
+        }
 
-lattice : Lattice ℕ
-lattice = record
-    { _≈_ = _≡_
-    ; _⊔_ = _⊔_
-    ; _⊓_ = _⊓_
-    ; isLattice = isLattice
-    }
+    lattice : Lattice ℕ
+    lattice = record
+        { _≈_ = _≡_
+        ; _⊔_ = _⊔_
+        ; _⊓_ = _⊓_
+        ; isLattice = isLattice
+        }