------------------------------------------------------------------------
-- The Agda standard library
--
-- An example of how Algebra.IdempotentCommutativeMonoidSolver can be
-- used
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
module Algebra.Solver.IdempotentCommutativeMonoid.Example where
import Algebra.Solver.IdempotentCommutativeMonoid as ICM-Solver
open import Data.Bool.Base using (_∨_)
open import Data.Bool.Properties using (∨-idempotentCommutativeMonoid)
open import Data.Fin.Base using (zero; suc)
open import Data.Vec.Base using ([]; _∷_)
open import Relation.Binary.PropositionalEquality.Core using (_≡_)
open ICM-Solver ∨-idempotentCommutativeMonoid
test : ∀ x y z → (x ∨ y) ∨ (x ∨ z) ≡ (z ∨ y) ∨ x
test a b c = let _∨_ = _⊕_ in
prove 3 ((x ∨ y) ∨ (x ∨ z)) ((z ∨ y) ∨ x) (a ∷ b ∷ c ∷ [])
where
x = var zero
y = var (suc zero)
z = var (suc (suc zero))
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