Hint Rewrite @gather_prop5 using not_a_prop : gather_prop.
Hint Rewrite @sepcon_andp_prop @sepcon_andp_prop' : gather_prop.
(*Hint Rewrite <- sepcon_assoc : gather_prop.*)

Lemma go_lower_lem1:
forall (P1 P: Prop) (QR PQR: mpred),
(P1 -> prop P && QR |-- PQR) ->
(prop (P1 /\ P ) && QR |-- PQR).