Classical.Small.Structures.Semilattice¶

Level-fixed Semilattice¶

This is the Classical.Small.Structures.Semilattice module of the Agda Universal Algebra Library.

Specializes Classical.Structures.Semilattice to the 0ℓ–0ℓ case, mirroring the veneers of Magma, Semigroup, CommutativeSemigroup, etc.

{-# OPTIONS --cubical-compatible --exact-split --safe #-}
module Classical.Small.Structures.Semilattice where
open import Agda.Primitive                          using () renaming ( Set to Type )
open import Level                                   using ( 0ℓ ; suc )
open import Relation.Binary.PropositionalEquality   using ( _≡_ )
import Classical.Structures.Semilattice as Polymorphic

Semilattice : Type (suc 0ℓ)
Semilattice = Polymorphic.Semilattice 0ℓ 0ℓ

eqsToSemilattice : (A : Type 0ℓ) (_·_ : A → A → A)
  → (∀ a b c → (a · b) · c ≡ a · (b · c))
  → (∀ a b → a · b ≡ b · a)
  → (∀ a → a · a ≡ a)
  → Semilattice
eqsToSemilattice = Polymorphic.eqsToSemilattice