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Strengthen absorption laws

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If x \/ y is defined, x /\ (x \/ y) has to be defined,
too. Previously, we stated them in terms of
"if x /\ (x \/ y) is defined", which is not right.

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin 2025-07-11 15:44:29 +02:00
parent d2faada90a
commit c1c34c69a5
1 changed files with 2 additions and 6 deletions
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8
Lattice/Builder.agda
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@ -129,10 +129,6 @@ record IsPartialSemilattice {a} {A : Set a}
x-identityʳ : (a : A) → (a ⊔? x) ≈? just a x-identityʳ : (a : A) → (a ⊔? x) ≈? just a
x-identityʳ a = ≈?-trans (⊔-comm a x) (x-identityˡ 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-≈ _≈_ (just a₁) a₂ = a₁ ≈ a₂
Maybe-≈ {a} _≈_ nothing a₂ = Trivial a
record IsPartialLattice {a} {A : Set a} record IsPartialLattice {a} {A : Set a}
(_≈_ : A → A → Set a) (_≈_ : A → A → Set a)
(_⊔?_ : A → A → Maybe A) (_⊔?_ : A → A → Maybe A)
@ -142,8 +138,8 @@ record IsPartialLattice {a} {A : Set a}
{{partialJoinSemilattice}} : IsPartialSemilattice _≈_ _⊔?_ {{partialJoinSemilattice}} : IsPartialSemilattice _≈_ _⊔?_
{{partialMeetSemilattice}} : IsPartialSemilattice _≈_ _⊓?_ {{partialMeetSemilattice}} : IsPartialSemilattice _≈_ _⊓?_
absorb-⊔-⊓ : (x y : A) → Maybe-≈ _≈_ ((x ⊓? y) >>= (x ⊔?_)) x absorb-⊔-⊓ : (x y : A) → maybe (λ x⊓y → lift-≈ _≈_ (x ⊔? x⊓y) (just x)) (Trivial _) (x ⊓? y)
absorb-⊓-⊔ : (x y : A) → Maybe-≈ _≈_ ((x ⊔? y) >>= (x ⊓?_)) x absorb-⊓-⊔ : (x y : A) → maybe (λ x⊔y → lift-≈ _≈_ (x ⊓? x⊔y) (just x)) (Trivial _) (x ⊔? y)
open IsPartialSemilattice partialJoinSemilattice public open IsPartialSemilattice partialJoinSemilattice public
open IsPartialSemilattice partialMeetSemilattice using () open IsPartialSemilattice partialMeetSemilattice using ()