Commit 18f83bcb by Robbert Krebbers

### Add class `Involutive`.

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