Commit 18f83bcb authored by Robbert Krebbers's avatar Robbert Krebbers
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Add class `Involutive`.

parent 77eecb3c

theories/base.v

+3 −0
Original line number Diff line number Diff line
@@ -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.