From d280f5afdf3ef4370418d5482d690df4d0c076bd Mon Sep 17 00:00:00 2001 From: Danila Fedorin Date: Sun, 25 Feb 2024 14:06:45 -0800 Subject: [PATCH] Make auxillary definitions private Signed-off-by: Danila Fedorin --- Isomorphism.agda | 29 +++++++++++++++-------------- 1 file changed, 15 insertions(+), 14 deletions(-) diff --git a/Isomorphism.agda b/Isomorphism.agda index 99a7efb..59e37ff 100644 --- a/Isomorphism.agda +++ b/Isomorphism.agda @@ -31,25 +31,26 @@ module TransportFiniteHeight open import Chain _≈₁_ ≈₁-equiv _≺₁_ ≺₁-cong using () renaming (Chain to Chain₁; done to done₁; step to step₁) open import Chain _≈₂_ ≈₂-equiv _≺₂_ ≺₂-cong using () renaming (Chain to Chain₂; done to done₂; step to step₂) - f-Injective : Injective _≈₁_ _≈₂_ f - f-Injective {x} {y} fx≈fy = ≈₁-trans (≈₁-sym (inverseʳ x)) (≈₁-trans (g-preserves-≈₂ fx≈fy) (inverseʳ y)) + private + f-Injective : Injective _≈₁_ _≈₂_ f + f-Injective {x} {y} fx≈fy = ≈₁-trans (≈₁-sym (inverseʳ x)) (≈₁-trans (g-preserves-≈₂ fx≈fy) (inverseʳ y)) - g-Injective : Injective _≈₂_ _≈₁_ g - g-Injective {x} {y} gx≈gy = ≈₂-trans (≈₂-sym (inverseˡ x)) (≈₂-trans (f-preserves-≈₁ gx≈gy) (inverseˡ y)) + g-Injective : Injective _≈₂_ _≈₁_ g + g-Injective {x} {y} gx≈gy = ≈₂-trans (≈₂-sym (inverseˡ x)) (≈₂-trans (f-preserves-≈₁ gx≈gy) (inverseˡ y)) - f-preserves-̷≈ : f Preserves (λ x y → ¬ x ≈₁ y) ⟶ (λ x y → ¬ x ≈₂ y) - f-preserves-̷≈ x̷≈y = λ fx≈fy → x̷≈y (f-Injective fx≈fy) + f-preserves-̷≈ : f Preserves (λ x y → ¬ x ≈₁ y) ⟶ (λ x y → ¬ x ≈₂ y) + f-preserves-̷≈ x̷≈y = λ fx≈fy → x̷≈y (f-Injective fx≈fy) - g-preserves-̷≈ : g Preserves (λ x y → ¬ x ≈₂ y) ⟶ (λ x y → ¬ x ≈₁ y) - g-preserves-̷≈ x̷≈y = λ gx≈gy → x̷≈y (g-Injective gx≈gy) + g-preserves-̷≈ : g Preserves (λ x y → ¬ x ≈₂ y) ⟶ (λ x y → ¬ x ≈₁ y) + g-preserves-̷≈ x̷≈y = λ gx≈gy → x̷≈y (g-Injective gx≈gy) - portChain₁ : ∀ {a₁ a₂ : A} {h : ℕ} → Chain₁ a₁ a₂ h → Chain₂ (f a₁) (f a₂) h - portChain₁ (done₁ a₁≈a₂) = done₂ (f-preserves-≈₁ a₁≈a₂) - portChain₁ (step₁ {a₁} {a₂} (a₁≼a₂ , a₁̷≈a₂) a₂≈a₂' c) = step₂ (≈₂-trans (≈₂-sym (f-⊔-distr a₁ a₂)) (f-preserves-≈₁ a₁≼a₂) , f-preserves-̷≈ a₁̷≈a₂) (f-preserves-≈₁ a₂≈a₂') (portChain₁ c) + portChain₁ : ∀ {a₁ a₂ : A} {h : ℕ} → Chain₁ a₁ a₂ h → Chain₂ (f a₁) (f a₂) h + portChain₁ (done₁ a₁≈a₂) = done₂ (f-preserves-≈₁ a₁≈a₂) + portChain₁ (step₁ {a₁} {a₂} (a₁≼a₂ , a₁̷≈a₂) a₂≈a₂' c) = step₂ (≈₂-trans (≈₂-sym (f-⊔-distr a₁ a₂)) (f-preserves-≈₁ a₁≼a₂) , f-preserves-̷≈ a₁̷≈a₂) (f-preserves-≈₁ a₂≈a₂') (portChain₁ c) - portChain₂ : ∀ {b₁ b₂ : B} {h : ℕ} → Chain₂ b₁ b₂ h → Chain₁ (g b₁) (g b₂) h - portChain₂ (done₂ a₂≈a₁) = done₁ (g-preserves-≈₂ a₂≈a₁) - portChain₂ (step₂ {b₁} {b₂} (b₁≼b₂ , b₁̷≈b₂) b₂≈b₂' c) = step₁ (≈₁-trans (≈₁-sym (g-⊔-distr b₁ b₂)) (g-preserves-≈₂ b₁≼b₂) , g-preserves-̷≈ b₁̷≈b₂) (g-preserves-≈₂ b₂≈b₂') (portChain₂ c) + portChain₂ : ∀ {b₁ b₂ : B} {h : ℕ} → Chain₂ b₁ b₂ h → Chain₁ (g b₁) (g b₂) h + portChain₂ (done₂ a₂≈a₁) = done₁ (g-preserves-≈₂ a₂≈a₁) + portChain₂ (step₂ {b₁} {b₂} (b₁≼b₂ , b₁̷≈b₂) b₂≈b₂' c) = step₁ (≈₁-trans (≈₁-sym (g-⊔-distr b₁ b₂)) (g-preserves-≈₂ b₁≼b₂) , g-preserves-̷≈ b₁̷≈b₂) (g-preserves-≈₂ b₂≈b₂') (portChain₂ c) isFiniteHeightLattice : IsFiniteHeightLattice B height _≈₂_ _⊔₂_ _⊓₂_ isFiniteHeightLattice =