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

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

Chain.agda

@@ -10,7 +10,7 @@ open import Data.Nat using (ℕ; suc; _+_; _≤_)
 open import Data.Nat.Properties using (+-comm; m+1+n≰m)
 open import Data.Product using (_×_; Σ; _,_)
 open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl)
-open import Data.Empty using (⊥)
+open import Data.Empty as Empty using ()
 
 open IsEquivalence ≈-equiv
 
@@ -38,11 +38,16 @@ module _  where
     Bounded : ℕ → Set a
     Bounded bound = ∀ {a₁ a₂ : A} {n : ℕ} → Chain a₁ a₂ n → n ≤ bound
 
-    Bounded-suc-n : ∀ {a₁ a₂ : A} {n : ℕ} → Bounded n → Chain a₁ a₂ (suc n) → ⊥
+    Bounded-suc-n : ∀ {a₁ a₂ : A} {n : ℕ} → Bounded n → Chain a₁ a₂ (suc n) → Empty.⊥
     Bounded-suc-n {a₁} {a₂} {n} bounded c = (m+1+n≰m n n+1≤n)
         where
             n+1≤n : n + 1 ≤ n
             n+1≤n rewrite (+-comm n 1) = bounded c
 
-    Height : ℕ → Set a
-    Height height = (Σ (A × A) (λ (a₁ , a₂) → Chain a₁ a₂ height) × Bounded height)
+    record Height (height : ℕ) : Set a where
+        field
+            ⊥ : A
+            ⊤ : A
+
+            longestChain : Chain ⊥ ⊤ height
+            bounded : Bounded height