Instance mkPX_ext : Proper (Pequiv ==> eq ==> Pequiv ==> Pequiv) mkPX.(* Quicker than autorewrite with Esimpl :-) *)
 Ltac Esimpl := try rewrite_db Esimpl; rsimpl; simpl.

Lemma zmon_pred_ok M j l : (zmon_pred j M) @@ (tail l) == (zmon j M) @@ l.