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Add a left and right version of identity

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2025-07-11 15:43:27 +02:00
parent 7fdbf0397d
commit d2faada90a
1 changed files with 4 additions and 1 deletions
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Lattice/Builder.agda
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@ -124,7 +124,10 @@ record IsPartialSemilattice {a} {A : Set a}
field field
x : A x : A
not-partial : ∀ (a₁ a₂ : A) → Σ A (λ a₃ → (a₁ ⊔? a₂) ≡ just a₃) not-partial : ∀ (a₁ a₂ : A) → Σ A (λ a₃ → (a₁ ⊔? a₂) ≡ just a₃)
x-identity : (a : A) → (x ⊔? a) ≈? just a x-identityˡ : (a : A) → (x ⊔? a) ≈? just a
x-identityʳ : (a : A) → (a ⊔? x) ≈? just a
x-identityʳ a = ≈?-trans (⊔-comm a x) (x-identityˡ a)
Maybe-≈ : ∀ {a} {A : Set a} → (_≈_ : A → A → Set a) → Maybe A → A → Set a Maybe-≈ : ∀ {a} {A : Set a} → (_≈_ : A → A → Set a) → Maybe A → A → Set a
Maybe-≈ _≈_ (just a₁) a₂ = a₁ ≈ a₂ Maybe-≈ _≈_ (just a₁) a₂ = a₁ ≈ a₂