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src/Algebra/Properties/Monoid/Reasoning.agda
@@ -8,10 +8,11 @@
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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra.Bundles using (Monoid)
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-open import Algebra.Structures using (IsMagma)
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module Algebra.Properties.Monoid.Reasoning {o ℓ} (M : Monoid o ℓ) where
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+open import Algebra.Structures using (IsMagma)
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+
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open Monoid M
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using (Carrier; _∙_; _≈_; setoid; isMagma; semigroup; ε; sym; identityˡ
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; identityʳ ; ∙-cong; refl; assoc; ∙-congˡ; ∙-congʳ; trans)
@@ -50,7 +51,7 @@ open IntroElim public
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module Cancellers {a b c : Carrier} (inv : a ∙ c ≈ ε) where
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- cancelʳ : (b ∙ a) ∙ c ≈ b
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+ cancelʳ : (b ∙ a) ∙ c ≈ b
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cancelʳ = trans (assoc b a c) (trans (∙-congˡ inv) (identityʳ b))
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cancelˡ : a ∙ (c ∙ b) ≈ b
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