Add PersistentP instances for own(S).

Initial proof by Jan-Oliver Kaiser, adapted by Robbert Krebbers.

algebra/sts.v

@@ -376,6 +376,11 @@ Proof.
     eapply closed_steps, Hsup; first done. set_solver +Hs'.
 Qed.
 
+Global Instance sts_frag_peristent S : Persistent (sts_frag S ∅).
+Proof.
+  constructor; split=> //= [[??]]. by rewrite /dra.dra_core /= sts.up_closed.
+Qed.
+
 (** Inclusion *)
 (* This is surprisingly different from to_validity_included. I am not sure
    whether this is because to_validity_included is non-canonical, or this

program_logic/sts.v

@@ -44,6 +44,10 @@ Section definitions.
   Proof. solve_proper. Qed.
   Global Instance sts_ctx_persistent N φ : PersistentP (sts_ctx N φ).
   Proof. apply _. Qed.
+  Global Instance sts_own_peristent s : PersistentP (sts_own s ∅).
+  Proof. apply _. Qed.
+  Global Instance sts_ownS_peristent S : PersistentP (sts_ownS S ∅).
+  Proof. apply _. Qed.
 End definitions.
 
 Typeclasses Opaque sts_own sts_ownS sts_inv sts_ctx.