Notation "'has_ view" := (hasPP _ (fun _ => view))
(at level 4, right associativity, format "''has_' view").
Notation "'all_ view" := (allPP _ (fun _ => view))
(at level 4, right associativity, format "''all_' view").
Section EqIn.
Variables a1 a2 : pred T.

Lemma has_sym s1 s2 : has (mem s1) s2 = has (mem s2) s1.