From 2ddac38c3f2335d0c010c6ee4b07c642a73de806 Mon Sep 17 00:00:00 2001
From: Danila Fedorin <danila.fedorin@gmail.com>
Date: Sun, 3 Mar 2024 16:44:10 -0800
Subject: [PATCH] Update with new changes to Agda

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
---
 Isomorphism.agda            | 14 ++++++++++++--
 Lattice/FiniteValueMap.agda |  9 +++++----
 Lattice/Prod.agda           |  2 +-
 3 files changed, 18 insertions(+), 7 deletions(-)

diff --git a/Isomorphism.agda b/Isomorphism.agda
index 454bf93..5e731ec 100644
--- a/Isomorphism.agda
+++ b/Isomorphism.agda
@@ -1,7 +1,7 @@
 module Isomorphism where
 
 open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔ℓ_)
-open import Function.Definitions using (Inverseˡ; Inverseʳ; Injective)
+open import Function.Definitions using (Injective)
 open import Lattice
 open import Equivalence
 open import Relation.Binary.Core using (_Preserves_⟶_ )
@@ -9,6 +9,16 @@ open import Data.Nat using (ℕ)
 open import Data.Product using (_,_)
 open import Relation.Nullary using (¬_)
 
+IsInverseˡ : ∀ {a b} {A : Set a} {B : Set b}
+               (_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set b)
+               (f : A → B) (g : B → A) → Set b
+IsInverseˡ {A = A} {B = B} _≈₁_ _≈₂_ f g = ∀ (x : B) → f (g x) ≈₂ x
+
+IsInverseʳ : ∀ {a b} {A : Set a} {B : Set b}
+               (_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set b)
+               (f : A → B) (g : B → A) → Set a
+IsInverseʳ {A = A} {B = B} _≈₁_ _≈₂_ f g = ∀ (x : A) → g (f x) ≈₁ x
+
 module TransportFiniteHeight
          {a b : Level} {A : Set a} {B : Set b}
          {_≈₁_ : A → A → Set a} {_≈₂_ : B → B → Set b}
@@ -20,7 +30,7 @@ module TransportFiniteHeight
          (f-preserves-≈₁ : f Preserves _≈₁_ ⟶  _≈₂_) (g-preserves-≈₂ : g Preserves _≈₂_ ⟶  _≈₁_)
          (f-⊔-distr : ∀ (a₁ a₂ : A) → f (a₁ ⊔₁ a₂) ≈₂ ((f a₁) ⊔₂ (f a₂)))
          (g-⊔-distr : ∀ (b₁ b₂ : B) → g (b₁ ⊔₂ b₂) ≈₁ ((g b₁) ⊔₁ (g b₂)))
-         (inverseˡ : Inverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : Inverseʳ _≈₁_ _≈₂_ f g) where
+         (inverseˡ : IsInverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : IsInverseʳ _≈₁_ _≈₂_ f g) where
 
     open IsFiniteHeightLattice fhlA using () renaming (_≺_ to _≺₁_; ≺-cong to ≺₁-cong; ≈-equiv to ≈₁-equiv)
     open IsLattice lB               using () renaming (_≺_ to _≺₂_; ≺-cong to ≺₂-cong; ≈-equiv to ≈₂-equiv)
diff --git a/Lattice/FiniteValueMap.agda b/Lattice/FiniteValueMap.agda
index 32bda52..9d9b9ca 100644
--- a/Lattice/FiniteValueMap.agda
+++ b/Lattice/FiniteValueMap.agda
@@ -27,6 +27,7 @@ open import Data.List.Properties using (∷-injectiveʳ)
 open import Data.List.Relation.Unary.All using (All)
 open import Data.List.Relation.Unary.Any using (Any; here; there)
 open import Relation.Nullary using (¬_)
+open import Isomorphism using (IsInverseˡ; IsInverseʳ)
 
 open import Lattice.Map A B _≈₂_ _⊔₂_ _⊓₂_ ≡-dec-A lB
     using
@@ -105,8 +106,8 @@ module IterProdIsomorphism where
 
     -- The left inverse is: from (to x) = x
     from-to-inverseˡ : ∀ {ks : List A} (uks : Unique ks) →
-                      Inverseˡ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
-                               (from {ks}) (to {ks} uks)
+                      IsInverseˡ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
+                                 (from {ks}) (to {ks} uks)
     from-to-inverseˡ {[]} _ _ = IsEquivalence.≈-refl (IP.≈-equiv 0)
     from-to-inverseˡ {k ∷ ks'} (push k≢ks' uks') (v , rest)
         with ((fm' , ufm') , refl) ← to uks' rest in p rewrite sym p =
@@ -121,8 +122,8 @@ module IterProdIsomorphism where
     --
     -- The right inverse is: to (from x) = x
     from-to-inverseʳ : ∀ {ks : List A} (uks : Unique ks) →
-                       Inverseʳ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
-                                (from {ks}) (to {ks} uks)
+                       IsInverseʳ (_≈ᵐ_ {ks}) (_≈ⁱᵖ_ {length ks})
+                                  (from {ks}) (to {ks} uks)
     from-to-inverseʳ {[]} _ (([] , empty) , kvs≡ks) rewrite kvs≡ks =
         ( (λ k v ())
         , (λ k v ())
diff --git a/Lattice/Prod.agda b/Lattice/Prod.agda
index 54fe15d..4b6d330 100644
--- a/Lattice/Prod.agda
+++ b/Lattice/Prod.agda
@@ -168,7 +168,7 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
                                  ))
         ...   | no a₁̷≈a  | no b₁̷≈b | ((n₁ , n₂) , ((c₁ , c₂) , n≤n₁+n₂)) =
                 ((suc n₁ , suc n₂) , ( (step₁ (a₁≼a , a₁̷≈a) a≈a' c₁ , step₂ (b₁≼b , b₁̷≈b) b≈b' c₂)
-                                     , ≤-stepsˡ 1 (subst (n ≤_) (sym (+-suc n₁ n₂)) (+-monoʳ-≤ 1 n≤n₁+n₂))
+                                     , m≤n⇒m≤o+n 1 (subst (n ≤_) (sym (+-suc n₁ n₂)) (+-monoʳ-≤ 1 n≤n₁+n₂))
                                      ))
 
     fixedHeight : IsLattice.FixedHeight isLattice (h₁ + h₂)