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Provide a 'fixed height' predicate from Lattice for convenience

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
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Danila Fedorin 2023-09-23 16:20:58 -07:00
parent dce21b3696
commit 8eaec3facd
1 changed files with 5 additions and 1 deletions
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Lattice.agda
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@ -77,6 +77,9 @@ record IsLattice {a} (A : Set a)
; ≼-refl to ≽-refl ; ≼-refl to ≽-refl
) )
FixedHeight : ∀ (h : ℕ) → Set a
FixedHeight h = Chain.Height (_≈_) ≈-equiv _≺_ ≺-cong h
record IsFiniteHeightLattice {a} (A : Set a) record IsFiniteHeightLattice {a} (A : Set a)
(h : ℕ) (h : ℕ)
(_≈_ : A → A → Set a) (_≈_ : A → A → Set a)
@ -85,10 +88,11 @@ record IsFiniteHeightLattice {a} (A : Set a)
field field
isLattice : IsLattice A _≈_ _⊔_ _⊓_ isLattice : IsLattice A _≈_ _⊔_ _⊓_
fixedHeight : Chain.Height (_≈_) (IsLattice.≈-equiv isLattice) (IsLattice._≺_ isLattice) (IsLattice.≺-cong isLattice) h
open IsLattice isLattice public open IsLattice isLattice public
field
fixedHeight : FixedHeight h
module _ {a b} {A : Set a} {B : Set b} module _ {a b} {A : Set a} {B : Set b}
(_≼₁_ : A → A → Set a) (_≼₂_ : B → B → Set b) where (_≼₁_ : A → A → Set a) (_≼₂_ : B → B → Set b) where