Commit 18f83bcb by Robbert Krebbers

parent 77eecb3c
 ... ... @@ -327,6 +327,8 @@ Class Trichotomy {A} (R : relation A) := trichotomy x y : R x y ∨ x = y ∨ R y x. Class TrichotomyT {A} (R : relation A) := trichotomyT x y : {R x y} + {x = y} + {R y x}. Class Involutive {A} (R : relation A) (f : A → A) := involutive x : R (f (f x)) x. Arguments irreflexivity {_} _ {_} _ _ : assert. Arguments inj {_ _ _ _} _ {_} _ _ _ : assert. ... ... @@ -344,6 +346,7 @@ Arguments anti_symm {_ _} _ {_} _ _ _ _ : assert. Arguments total {_} _ {_} _ _ : assert. Arguments trichotomy {_} _ {_} _ _ : assert. Arguments trichotomyT {_} _ {_} _ _ : assert. Arguments involutive {_ _} _ {_} _ : assert. Lemma not_symmetry `{R : relation A, !Symmetric R} x y : ¬R x y → ¬R y x. Proof. intuition. Qed. ... ...
• Owner

Isn't it a bit strange to have a class with 0 instances in the library?

• Maintainer

I suppose we could add an instance for negation of integers?

• Owner

Looking at the other classes, isn't `Involutive R f` the same as `Cancel R f f`?

Edited by Ralf Jung
• Owner

I was also about to suggest a relation to idempotency, which I thought was something like `f (f x) = f x`, but it doesn't seem like we have that? We work with such a function a lot though, it's called the core. (Well, things get more complicated because that can also be partial.)

We only have `f x x = x`, which is an idempotent element of an operation, but not an idempotent operation.

Edited by Ralf Jung
• Maintainer

Looking at the other classes, isn't `Involutive R f` the same as `Cancel R f f`?

Good point, maybe we should just make it a notation for that?

• Maintainer

I was also about to suggest a relation to idempotency,

Not sure if that's worth it.

• mentioned in merge request !79 (merged)

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