Try to generalize universe levels where possible
Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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open import Lattice
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-- Due to universe levels, it becomes relatively annoying to handle the case
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-- where the levels of A and B are not the same. For the time being, constrain
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-- them to be the same.
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module Lattice.IterProd {a} {A B : Set a}
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(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set a)
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(_⊔₁_ : A → A → A) (_⊔₂_ : B → B → B)
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open import Lattice
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module Lattice.Prod {a} {A B : Set a}
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(_≈₁_ : A → A → Set a) (_≈₂_ : B → B → Set a)
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module Lattice.Prod {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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(_⊔₁_ : A → A → A) (_⊔₂_ : B → B → B)
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(_⊓₁_ : A → A → A) (_⊓₂_ : B → B → B)
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(lA : IsLattice A _≈₁_ _⊔₁_ _⊓₁_) (lB : IsLattice B _≈₂_ _⊔₂_ _⊓₂_) where
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open import Agda.Primitive using (Level) renaming (_⊔_ to _⊔ℓ_)
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open import Data.Nat using (ℕ; _≤_; _+_; suc)
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open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂)
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open import Data.Empty using (⊥-elim)
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@ -35,7 +36,7 @@ open IsLattice lB using () renaming
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; ≺-cong to ≺₂-cong
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)
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_≈_ : A × B → A × B → Set a
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_≈_ : A × B → A × B → Set (a ⊔ℓ b)
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(a₁ , b₁) ≈ (a₂ , b₂) = (a₁ ≈₁ a₂) × (b₁ ≈₂ b₂)
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≈-equiv : IsEquivalence (A × B) _≈_
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