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Match on _IsRelatedTo_ later for the PartialSetoid Reasoning #2677

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Match on _IsRelatedTo_ later for the PartialSetoid Reasoning #2677

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7 changes: 5 additions & 2 deletions src/Relation/Binary/Reasoning/Base/Partial.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -31,9 +31,12 @@ data _IsRelatedTo_ : A → A → Set (a ⊔ ℓ) where
singleStep : ∀ x → x IsRelatedTo x
multiStep : ∀ {x y} (x∼y : x ∼ y) → x IsRelatedTo y

∼-go-build : Trans _∼_ _IsRelatedTo_ _∼_
∼-go-build x∼y (singleStep y) = x∼y
∼-go-build x∼y (multiStep y∼z) = trans x∼y y∼z

∼-go : Trans _∼_ _IsRelatedTo_ _IsRelatedTo_
∼-go x∼y (singleStep y) = multiStep x∼y
∼-go x∼y (multiStep y∼z) = multiStep (trans x∼y y∼z)
∼-go x∼y y<z = multiStep (∼-go-build x∼y y<z)

stop : Reflexive _IsRelatedTo_
stop = singleStep _
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