Use records rather than nested pairs to represent 'fixed height'

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

Isomorphism.agda

@@ -38,8 +38,9 @@ module TransportFiniteHeight
     open IsEquivalence ≈₁-equiv using () renaming (≈-sym to ≈₁-sym; ≈-trans to ≈₁-trans)
     open IsEquivalence ≈₂-equiv using () renaming (≈-sym to ≈₂-sym; ≈-trans to ≈₂-trans)
 
-    open import Chain _≈₁_ ≈₁-equiv _≺₁_ ≺₁-cong using () renaming (Chain to Chain₁; done to done₁; step to step₁)
-    open import Chain _≈₂_ ≈₂-equiv _≺₂_ ≺₂-cong using () renaming (Chain to Chain₂; done to done₂; step to step₂)
+    import Chain
+    open Chain _≈₁_ ≈₁-equiv _≺₁_ ≺₁-cong using () renaming (Chain to Chain₁; done to done₁; step to step₁)
+    open Chain _≈₂_ ≈₂-equiv _≺₂_ ≺₂-cong using () renaming (Chain to Chain₂; done to done₂; step to step₂)
 
     private
         f-Injective : Injective _≈₁_ _≈₂_ f
@@ -65,10 +66,17 @@ module TransportFiniteHeight
     isFiniteHeightLattice : IsFiniteHeightLattice B height _≈₂_ _⊔₂_ _⊓₂_
     isFiniteHeightLattice =
         let
-            (((a₁ , a₂) , c) , bounded₁) = IsFiniteHeightLattice.fixedHeight fhlA
+            open Chain.Height (IsFiniteHeightLattice.fixedHeight fhlA)
+                using ()
+                renaming (⊥ to ⊥₁; ⊤ to ⊤₁; bounded to bounded₁; longestChain to c)
         in record
             { isLattice = lB
-            ; fixedHeight = (((f a₁ , f a₂), portChain₁ c) , λ c' → bounded₁ (portChain₂ c'))
+            ; fixedHeight = record
+                { ⊥ = f ⊥₁
+                ; ⊤ = f ⊤₁
+                ; longestChain = portChain₁ c
+                ; bounded = λ c' → bounded₁ (portChain₂ c')
+                }
             }
 
     finiteHeightLattice : FiniteHeightLattice B