Update with new changes to Agda
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@@ -1,7 +1,7 @@
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module Isomorphism where
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open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔ℓ_)
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open import Function.Definitions using (Inverseˡ; Inverseʳ; Injective)
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open import Function.Definitions using (Injective)
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open import Lattice
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open import Equivalence
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open import Relation.Binary.Core using (_Preserves_⟶_ )
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@@ -9,6 +9,16 @@ open import Data.Nat using (ℕ)
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open import Data.Product using (_,_)
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open import Relation.Nullary using (¬_)
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IsInverseˡ : ∀ {a b} {A : Set a} {B : Set b}
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(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set b)
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(f : A → B) (g : B → A) → Set b
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IsInverseˡ {A = A} {B = B} _≈₁_ _≈₂_ f g = ∀ (x : B) → f (g x) ≈₂ x
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IsInverseʳ : ∀ {a b} {A : Set a} {B : Set b}
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(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set b)
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(f : A → B) (g : B → A) → Set a
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IsInverseʳ {A = A} {B = B} _≈₁_ _≈₂_ f g = ∀ (x : A) → g (f x) ≈₁ x
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module TransportFiniteHeight
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{a b : Level} {A : Set a} {B : Set b}
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{_≈₁_ : A → A → Set a} {_≈₂_ : B → B → Set b}
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@@ -20,7 +30,7 @@ module TransportFiniteHeight
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(f-preserves-≈₁ : f Preserves _≈₁_ ⟶ _≈₂_) (g-preserves-≈₂ : g Preserves _≈₂_ ⟶ _≈₁_)
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(f-⊔-distr : ∀ (a₁ a₂ : A) → f (a₁ ⊔₁ a₂) ≈₂ ((f a₁) ⊔₂ (f a₂)))
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(g-⊔-distr : ∀ (b₁ b₂ : B) → g (b₁ ⊔₂ b₂) ≈₁ ((g b₁) ⊔₁ (g b₂)))
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(inverseˡ : Inverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : Inverseʳ _≈₁_ _≈₂_ f g) where
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(inverseˡ : IsInverseˡ _≈₁_ _≈₂_ f g) (inverseʳ : IsInverseʳ _≈₁_ _≈₂_ f g) where
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open IsFiniteHeightLattice fhlA using () renaming (_≺_ to _≺₁_; ≺-cong to ≺₁-cong; ≈-equiv to ≈₁-equiv)
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open IsLattice lB using () renaming (_≺_ to _≺₂_; ≺-cong to ≺₂-cong; ≈-equiv to ≈₂-equiv)
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