Local Open Scope logic.
Definition nonlocal (Q: environ->mpred) := True.
Ltac check_nonlocal :=
match goal with
|  |- nonlocal (local _) => fail 1
|  |- nonlocal (prop _) => fail 1
|  |- nonlocal (andp _ _) => fail 1
|  |- nonlocal (sepcon _ _) => fail 1
| |- _ => apply I
end.
Hint Rewrite canon1 canon2 canon4 canon8 : canon.
Hint Rewrite canon3 using check_nonlocal : canon.
Hint Rewrite canon3b using check_nonlocal : canon.
Hint Rewrite canon7 using check_nonlocal : canon.
Hint Rewrite <- (@sepcon_assoc (environ->mpred) _) : canon.

Lemma canon5: forall Q R S,
nonlocal Q ->
Q && (local R && S) = local R && (Q && S).