@@ -746,7 +746,7 @@ neg⇒nonZero (mkℚᵘ (-[1+ _ ]) _) = _
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+-identityˡ p = ≃-reflexive (+-identityˡ-≡ p)
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+-identityʳ-≡ : RightIdentity _≡_ 0ℚᵘ _+_
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- +-identityʳ-≡ = comm+ idˡ⇒idʳ +-comm-≡ {e = 0ℚᵘ} +-identityˡ-≡
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+ +-identityʳ-≡ = comm∧ idˡ⇒idʳ +-comm-≡ {e = 0ℚᵘ} +-identityˡ-≡
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+-identityʳ : RightIdentity _≃_ 0ℚᵘ _+_
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+-identityʳ p = ≃-reflexive (+-identityʳ-≡ p)
@@ -1104,7 +1104,7 @@ p≤q⇒0≤q-p {p} {q} p≤q = begin
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*-identityˡ-≡ p@record{} = ↥↧≡⇒≡ (ℤ.*-identityˡ (↥ p)) (ℕ.+-identityʳ (↧ₙ p))
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*-identityʳ-≡ : RightIdentity _≡_ 1ℚᵘ _*_
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- *-identityʳ-≡ = comm+ idˡ⇒idʳ *-comm-≡ {e = 1ℚᵘ} *-identityˡ-≡
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+ *-identityʳ-≡ = comm∧ idˡ⇒idʳ *-comm-≡ {e = 1ℚᵘ} *-identityˡ-≡
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*-identity-≡ : Identity _≡_ 1ℚᵘ _*_
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*-identity-≡ = *-identityˡ-≡ , *-identityʳ-≡
@@ -1144,7 +1144,7 @@ p≤q⇒0≤q-p {p} {q} p≤q = begin
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*-zeroˡ p@record{} = *≡* refl
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*-zeroʳ : RightZero _≃_ 0ℚᵘ _*_
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- *-zeroʳ = Consequences.comm+ zeˡ⇒zeʳ ≃-setoid *-comm *-zeroˡ
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+ *-zeroʳ = Consequences.comm∧ zeˡ⇒zeʳ ≃-setoid *-comm *-zeroˡ
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*-zero : Zero _≃_ 0ℚᵘ _*_
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*-zero = *-zeroˡ , *-zeroʳ
@@ -1171,7 +1171,7 @@ invertible⇒≄ {p} {q} (1/p-q , 1/x*x≃1 , x*1/x≃1) p≃q = 0≄1 (begin
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in *≡* eq where open ℤ-solver
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*-distribʳ-+ : _DistributesOverʳ_ _≃_ _*_ _+_
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- *-distribʳ-+ = Consequences.comm+ distrˡ⇒distrʳ ≃-setoid +-cong *-comm *-distribˡ-+
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+ *-distribʳ-+ = Consequences.comm∧ distrˡ⇒distrʳ ≃-setoid +-cong *-comm *-distribˡ-+
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*-distrib-+ : _DistributesOver_ _≃_ _*_ _+_
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*-distrib-+ = *-distribˡ-+ , *-distribʳ-+
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