Update with new changes to Agda

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
2024-03-03 16:44:10 -08:00
parent f00dabfc93
commit 2ddac38c3f
3 changed files with 18 additions and 7 deletions

View File

@@ -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)