Provide a definition of partial congruence

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

Lattice/Builder.agda

@@ -3,6 +3,7 @@ module Lattice.Builder where
 open import Lattice
 open import Equivalence
 open import Data.Maybe as Maybe using (Maybe; just; nothing; _>>=_; maybe)
+open import Data.Maybe.Properties using (just-injective)
 open import Data.Unit using (⊤; tt)
 open import Data.List.NonEmpty using (List⁺; tail; toList) renaming (_∷_ to _∷⁺_)
 open import Data.List using (List; _∷_; [])
@@ -42,6 +43,9 @@ instance
                      }
         }
 
+PartialCong : ∀ {a} {A : Set a} (_≈_ : A → A → Set a) (_⊗_ : A → A → Maybe A) → Set a
+PartialCong {a} {A} _≈_ _⊗_ = ∀ {a₁ a₂ a₃ a₄} → a₁ ≈ a₂ → a₃ ≈ a₄ → lift-≈ _≈_ (a₁ ⊗ a₃) (a₂ ⊗ a₄)
+
 PartialAssoc : ∀ {a} {A : Set a} (_≈_ : A → A → Set a) (_⊗_ : A → A → Maybe A) → Set a
 PartialAssoc {a} {A} _≈_ _⊗_ = ∀ (x y z : A) →  lift-≈ _≈_ ((x ⊗ y) >>= (_⊗ z)) ((y ⊗ z) >>= (x ⊗_))
 
@@ -69,7 +73,7 @@ record IsPartialSemilattice {a} {A : Set a}
 
     field
         ≈-equiv : IsEquivalence A _≈_
-        ≈-⊔-cong : ∀ {a₁ a₂ a₃ a₄} → a₁ ≈ a₂ → a₃ ≈ a₄ → (a₁ ⊔? a₃) ≈? (a₂ ⊔? a₄)
+        ≈-⊔-cong : PartialCong _≈_ _⊔?_
 
         ⊔-assoc : PartialAssoc _≈_ _⊔?_
         ⊔-comm : PartialComm _≈_ _⊔?_