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lines changed Original file line number Diff line number Diff line change @@ -133,6 +133,9 @@ module Section (≈₂ : Rel B ℓ₂) (surj : Surjective {A = A} ≈₁ ≈₂
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strictlyInverseˡ : StrictlyInverseˡ ≈₂ f section
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strictlyInverseˡ _ = inverseˡ refl
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+ strictlyInverseʳ : StrictlyInverseʳ ≈₂ section f
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+ strictlyInverseʳ _ = inverseˡ refl
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+
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injective : Symmetric ≈₂ → Transitive ≈₂ → Injective ≈₂ ≈₁ section
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injective sym trans = trans (sym (strictlyInverseˡ _)) ∘ inverseˡ
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@@ -146,9 +149,6 @@ module Section (≈₂ : Rel B ℓ₂) (surj : Surjective {A = A} ≈₁ ≈₂
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inverseʳ : Transitive ≈₂ → Inverseʳ ≈₁ ≈₂ f section
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inverseʳ trans = inj ∘ trans (f∘section≡id _)
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- strictlyInverseʳ : Transitive ≈₂ → StrictlyInverseʳ ≈₂ section f
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- strictlyInverseʳ trans = inverseʳ⇒strictlyInverseʳ ≈₂ ≈₁ refl inverseˡ
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-
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surjective : Transitive ≈₂ → Surjective ≈₂ ≈₁ section
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surjective trans x = f x , inverseʳ trans
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