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Define weak extensionality of a relation #596

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merged 2 commits into from
May 3, 2022

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shlevy
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@shlevy shlevy commented Aug 19, 2021

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@ecavallo
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How do you feel about this definition, which is better-behaved when the carrier is not a set:
https://github.com/ecavallo/cubical/blob/80383989d6bfbae6d50946b98d62dcd774c44d06/Cubical/Relation/Binary/Extensionality.agda?

isWeaklyExtensional : Type _
isWeaklyExtensional = ∀ {x y} → (∀ {z} → (z ≺ x → z ≺ y) × (z ≺ y → z ≺ x)) → x ≡ y

isWeaklyExtensional-isProp : isSet A → isProp isWeaklyExtensional
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Please rename to isPropIsWeaklyExtensional.

@ecavallo ecavallo merged commit eda9bfb into agda:master May 3, 2022
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2 participants