Instance pred_sepcon_proper: Proper (pointwise_relation B eq ==> pointwise_relation B iff ==> eq) pred_sepcon.

(* Specifications: *)
Lemma pred_sepcon1: forall p x0, pred_sepcon p (fun x => x = x0) = p x0.
Lemma pred_sepcon_False: forall p, pred_sepcon p (fun _ => False) = emp.