Rename the min/max elements top bottom and top in Prod
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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@ -143,17 +143,17 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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∙,b-Preserves-≈₁ : ∀ (b : B) → (λ a → (a , b)) Preserves _≈₁_ ⟶ _≈_
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∙,b-Preserves-≈₁ b {a₁} {a₂} a₁≈a₂ = (a₁≈a₂ , ≈₂-refl)
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amin : A
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amin = proj₁ (proj₁ (proj₁ fhA))
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⊥₁ : A
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⊥₁ = proj₁ (proj₁ (proj₁ fhA))
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amax : A
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amax = proj₂ (proj₁ (proj₁ fhA))
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⊤₁ : A
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⊤₁ = proj₂ (proj₁ (proj₁ fhA))
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bmin : B
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bmin = proj₁ (proj₁ (proj₁ fhB))
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⊥₂ : B
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⊥₂ = proj₁ (proj₁ (proj₁ fhB))
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bmax : B
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bmax = proj₂ (proj₁ (proj₁ fhB))
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⊤₂ : B
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⊤₂ = proj₂ (proj₁ (proj₁ fhB))
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unzip : ∀ {a₁ a₂ : A} {b₁ b₂ : B} {n : ℕ} → Chain (a₁ , b₁) (a₂ , b₂) n → Σ (ℕ × ℕ) (λ (n₁ , n₂) → ((Chain₁ a₁ a₂ n₁ × Chain₂ b₁ b₂ n₂) × (n ≤ n₁ + n₂)))
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unzip (done (a₁≈a₂ , b₁≈b₂)) = ((0 , 0) , ((done₁ a₁≈a₂ , done₂ b₁≈b₂) , ≤-refl))
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@ -173,10 +173,10 @@ module _ (≈₁-dec : IsDecidable _≈₁_) (≈₂-dec : IsDecidable _≈₂_)
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fixedHeight : IsLattice.FixedHeight isLattice (h₁ + h₂)
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fixedHeight =
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( ( ((amin , bmin) , (amax , bmax))
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( ( ((⊥₁ , ⊥₂) , (⊤₁ , ⊤₂))
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, concat
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(ChainMapping₁.Chain-map (λ a → (a , bmin)) (∙,b-Monotonic _) proj₁ (∙,b-Preserves-≈₁ _) (proj₂ (proj₁ fhA)))
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(ChainMapping₂.Chain-map (λ b → (amax , b)) (a,∙-Monotonic _) proj₂ (a,∙-Preserves-≈₂ _) (proj₂ (proj₁ fhB)))
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(ChainMapping₁.Chain-map (λ a → (a , ⊥₂)) (∙,b-Monotonic _) proj₁ (∙,b-Preserves-≈₁ _) (proj₂ (proj₁ fhA)))
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(ChainMapping₂.Chain-map (λ b → (⊤₁ , b)) (a,∙-Monotonic _) proj₂ (a,∙-Preserves-≈₂ _) (proj₂ (proj₁ fhB)))
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)
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, λ a₁b₁a₂b₂ → let ((n₁ , n₂) , ((a₁a₂ , b₁b₂) , n≤n₁+n₂)) = unzip a₁b₁a₂b₂
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in ≤-trans n≤n₁+n₂ (+-mono-≤ (proj₂ fhA a₁a₂) (proj₂ fhB b₁b₂))
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