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[ bug ] Fix use of + in lemma preconditions in favour of ∧ #2564

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Merged
merged 1 commit into from
Jan 25, 2025
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[ bug ] Fix use of + in lemma preconditions in favour of ∧ #2564

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4 changes: 2 additions & 2 deletions src/Data/Nat/Properties.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -17,7 +17,7 @@ open import Algebra.Bundles using (Magma; Semigroup; CommutativeSemigroup;
open import Algebra.Definitions.RawMagma using (_,_)
open import Algebra.Morphism
open import Algebra.Consequences.Propositional
using (comm+cancelˡ⇒cancelʳ; comm∧distrʳ⇒distrˡ; comm∧distrˡ⇒distrʳ)
using (comm∧cancelˡ⇒cancelʳ; comm∧distrʳ⇒distrˡ; comm∧distrˡ⇒distrʳ)
open import Algebra.Construct.NaturalChoice.Base
using (MinOperator; MaxOperator)
import Algebra.Construct.NaturalChoice.MinMaxOp as MinMaxOp
Expand Down Expand Up @@ -561,7 +561,7 @@ open ≤-Reasoning
+-cancelˡ-≡ (suc m) _ _ eq = +-cancelˡ-≡ m _ _ (cong pred eq)

+-cancelʳ-≡ : RightCancellative _≡_ _+_
+-cancelʳ-≡ = comm+cancelˡ⇒cancelʳ +-comm +-cancelˡ-≡
+-cancelʳ-≡ = comm∧cancelˡ⇒cancelʳ +-comm +-cancelˡ-≡

+-cancel-≡ : Cancellative _≡_ _+_
+-cancel-≡ = +-cancelˡ-≡ , +-cancelʳ-≡
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