Make progress on properties of the dependent product

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

Lattice.agda

@@ -237,13 +237,16 @@ record IsFiniteHeightLattice {a} (A : Set a)
     field
         {{fixedHeight}} : FixedHeight h
 
+    private
+        module MyChain = Chain _≈_ ≈-equiv _≺_ ≺-cong
+
+    open MyChain.Height fixedHeight using (⊥; ⊤) public
+
     -- If the equality is decidable, we can prove that the top and bottom
     -- elements of the chain are least and greatest elements of the lattice
     module _ {{≈-Decidable : IsDecidable _≈_}} where
         open IsDecidable ≈-Decidable using () renaming (R-dec to ≈-dec)
 
-        module MyChain = Chain _≈_ ≈-equiv _≺_ ≺-cong
-        open MyChain.Height fixedHeight using (⊥; ⊤) public
         open MyChain.Height fixedHeight using (bounded; longestChain)
 
         ⊥≼ : ∀ (a : A) → ⊥ ≼ a