Construct proofs of 'basic' lattices

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

Equivalence.agda

@@ -2,7 +2,7 @@ module Equivalence where
 
 open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂)
 open import Relation.Binary.Definitions
-open import Relation.Binary.PropositionalEquality as Eq using (_≡_; sym)
+open import Relation.Binary.PropositionalEquality as Eq using (_≡_; refl; sym; trans)
 
 module _ {a} (A : Set a) (_≈_ : A → A → Set a) where
     IsReflexive : Set a
@@ -19,3 +19,10 @@ module _ {a} (A : Set a) (_≈_ : A → A → Set a) where
             ≈-refl : IsReflexive
             ≈-sym : IsSymmetric
             ≈-trans : IsTransitive
+
+isEquivalence-≡ : ∀ {a} {A : Set a} → IsEquivalence A _≡_
+isEquivalence-≡ = record
+    { ≈-refl = refl
+    ; ≈-sym = sym
+    ; ≈-trans = trans
+    }