Move the lattice etc. instances into Lattice.Map

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

Lattice.agda

@@ -215,48 +215,6 @@ module IsSemilatticeInstances where
                 )
             }
 
-    module ForMap {a} {A B : Set a}
-        (≡-dec-A : Decidable (_≡_ {a} {A}))
-        (_≈₂_ : B → B → Set a)
-        (_⊔₂_ : B → B → B)
-        (sB : IsSemilattice B _≈₂_ _⊔₂_) where
-
-        open import Lattice.Map A B ≡-dec-A
-        open IsSemilattice sB renaming
-            ( ≈-refl to ≈₂-refl; ≈-sym to ≈₂-sym; ≈-⊔-cong to ≈₂-⊔₂-cong
-            ; ⊔-assoc to ⊔₂-assoc; ⊔-comm to ⊔₂-comm; ⊔-idemp to ⊔₂-idemp
-            )
-
-        module MapEquiv = IsEquivalenceInstances.ForMap A B ≡-dec-A _≈₂_ (IsSemilattice.≈-equiv sB)
-        open MapEquiv using (_≈_) public
-
-        infixl 20 _⊔_
-        infixl 20 _⊓_
-
-        _⊔_ : Map → Map → Map
-        m₁ ⊔ m₂ = union _⊔₂_ m₁ m₂
-
-        _⊓_ : Map → Map → Map
-        m₁ ⊓ m₂ = intersect _⊔₂_ m₁ m₂
-
-        MapIsUnionSemilattice : IsSemilattice Map _≈_ _⊔_
-        MapIsUnionSemilattice = record
-            { ≈-equiv = MapEquiv.LiftEquivalence
-            ; ≈-⊔-cong = λ {m₁} {m₂} {m₃} {m₄} → union-cong _≈₂_ _⊔₂_ ≈₂-⊔₂-cong {m₁} {m₂} {m₃} {m₄}
-            ; ⊔-assoc = union-assoc _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-assoc
-            ; ⊔-comm = union-comm _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-comm
-            ; ⊔-idemp = union-idemp _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-idemp
-            }
-
-        MapIsIntersectSemilattice : IsSemilattice Map _≈_ _⊓_
-        MapIsIntersectSemilattice = record
-            { ≈-equiv = MapEquiv.LiftEquivalence
-            ; ≈-⊔-cong = λ {m₁} {m₂} {m₃} {m₄} → intersect-cong _≈₂_ _⊔₂_ ≈₂-⊔₂-cong {m₁} {m₂} {m₃} {m₄}
-            ; ⊔-assoc = intersect-assoc _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-assoc
-            ; ⊔-comm = intersect-comm _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-comm
-            ; ⊔-idemp = intersect-idemp _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ ⊔₂-idemp
-            }
-
 module IsLatticeInstances where
     module ForNat where
         open Nat
@@ -329,33 +287,6 @@ module IsLatticeInstances where
                 )
             }
 
-    module ForMap {a} {A B : Set a}
-        (≡-dec-A : Decidable (_≡_ {a} {A}))
-        (_≈₂_ : B → B → Set a)
-        (_⊔₂_ : B → B → B)
-        (_⊓₂_ : B → B → B)
-        (lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_) where
-
-        open import Lattice.Map A B ≡-dec-A
-        open IsLattice lB renaming
-            ( ≈-refl to ≈₂-refl; ≈-sym to ≈₂-sym
-            ; ⊔-idemp to ⊔₂-idemp; ⊓-idemp to ⊓₂-idemp
-            ; absorb-⊔-⊓ to absorb-⊔₂-⊓₂; absorb-⊓-⊔ to absorb-⊓₂-⊔₂
-            )
-
-        module MapJoin = IsSemilatticeInstances.ForMap ≡-dec-A _≈₂_ _⊔₂_ (IsLattice.joinSemilattice lB)
-        open MapJoin using (_⊔_; _≈_) public
-
-        module MapMeet = IsSemilatticeInstances.ForMap ≡-dec-A _≈₂_ _⊓₂_ (IsLattice.meetSemilattice lB)
-        open MapMeet using (_⊓_) public
-
-        MapIsLattice : IsLattice Map _≈_ _⊔_ _⊓_
-        MapIsLattice = record
-            { joinSemilattice = MapJoin.MapIsUnionSemilattice
-            ; meetSemilattice = MapMeet.MapIsIntersectSemilattice
-            ; absorb-⊔-⊓ = union-intersect-absorb _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ _⊓₂_ ⊔₂-idemp ⊓₂-idemp absorb-⊔₂-⊓₂ absorb-⊓₂-⊔₂
-            ; absorb-⊓-⊔ = intersect-union-absorb _≈₂_ ≈₂-refl ≈₂-sym _⊔₂_ _⊓₂_ ⊔₂-idemp ⊓₂-idemp absorb-⊔₂-⊓₂ absorb-⊓₂-⊔₂
-            }
 
 module IsFiniteHeightLatticeInstances where
     module ForProd {a} {A B : Set a}