Migrate Maps to including a uniqueness proof

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
2023-07-24 23:55:09 -07:00
parent c2bc1c5421
commit 4aea9a0358
2 changed files with 43 additions and 26 deletions
--- a/Lattice.agda
+++ b/Lattice.agda
@@ -101,19 +101,22 @@ module IsEquivalenceInstances where
                in (v'' , (≈₂-trans v≈v' v'≈v'' , k,v''∈m₃))

            ≈-refl : {m : Map} → m ≈ m
-            ≈-refl {m} = (⊆-refl , ⊆-refl)
+            ≈-refl {m} = (⊆-refl {m}, ⊆-refl {m})

            ≈-sym : {m₁ m₂ : Map} → m₁ ≈ m₂ → m₂ ≈ m₁
            ≈-sym (m₁⊆m₂ , m₂⊆m₁) = (m₂⊆m₁ , m₁⊆m₂)

            ≈-trans : {m₁ m₂ m₃ : Map} → m₁ ≈ m₂ → m₂ ≈ m₃ → m₁ ≈ m₃
-            ≈-trans (m₁⊆m₂ , m₂⊆m₁) (m₂⊆m₃ , m₃⊆m₂) = (⊆-trans m₁⊆m₂ m₂⊆m₃ , ⊆-trans m₃⊆m₂ m₂⊆m₁)
+            ≈-trans {m₁} {m₂} {m₃} (m₁⊆m₂ , m₂⊆m₁) (m₂⊆m₃ , m₃⊆m₂) =
+                ( ⊆-trans {m₁} {m₂} {m₃} m₁⊆m₂ m₂⊆m₃
+                , ⊆-trans {m₃} {m₂} {m₁} m₃⊆m₂ m₂⊆m₁
+                )

            LiftEquivalence : IsEquivalence Map _≈_
            LiftEquivalence = record
-                { ≈-refl = ≈-refl
-                ; ≈-sym = ≈-sym
-                ; ≈-trans = ≈-trans
+                { ≈-refl = λ {m₁} → ≈-refl {m₁}
+                ; ≈-sym = λ {m₁} {m₂} → ≈-sym {m₁} {m₂}
+                ; ≈-trans = λ {m₁} {m₂} {m₃} → ≈-trans {m₁} {m₂} {m₃}
                }

 module IsSemilatticeInstances where