Commit 5e6e9a20 by Robbert

### Merge branch 'robbert/involutive' into 'master'

```Define `Involutive` in terms of `Cancel`.

See merge request iris/stdpp!79```
parents a426377a 9fbe44b6
 ... @@ -327,8 +327,11 @@ Class Trichotomy {A} (R : relation A) := ... @@ -327,8 +327,11 @@ 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. Notation Involutive R f := (Cancel R f f). Lemma involutive {A} {R : relation A} (f : A → A) `{Involutive R f} x : R (f (f x)) x. Proof. auto. Qed. Arguments irreflexivity {_} _ {_} _ _ : assert. Arguments irreflexivity {_} _ {_} _ _ : assert. Arguments inj {_ _ _ _} _ {_} _ _ _ : assert. Arguments inj {_ _ _ _} _ {_} _ _ _ : assert. ... @@ -346,7 +349,6 @@ Arguments anti_symm {_ _} _ {_} _ _ _ _ : assert. ... @@ -346,7 +349,6 @@ 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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