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1 parent 029f251 commit 87a3d6bCopy full SHA for 87a3d6b
src/Relation/Binary/Reasoning/Base/Partial.agda
@@ -31,9 +31,12 @@ data _IsRelatedTo_ : A → A → Set (a ⊔ ℓ) where
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singleStep : ∀ x → x IsRelatedTo x
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multiStep : ∀ {x y} (x∼y : x ∼ y) → x IsRelatedTo y
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+∼-go-build : Trans _∼_ _IsRelatedTo_ _∼_
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+∼-go-build x∼y (singleStep y) = x∼y
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+∼-go-build x∼y (multiStep y∼z) = trans x∼y y∼z
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+
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∼-go : Trans _∼_ _IsRelatedTo_ _IsRelatedTo_
-∼-go x∼y (singleStep y) = multiStep x∼y
-∼-go x∼y (multiStep y∼z) = multiStep (trans x∼y y∼z)
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+∼-go x∼y y<z = multiStep (∼-go-build x∼y y<z)
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stop : Reflexive _IsRelatedTo_
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stop = singleStep _
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