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.

Lemma canon3: forall R1 B P Q R,
nonlocal `(R1) ->
do_canon (B * `(R1)) (PROPx P (LOCALx Q (SEPx R))) = do_canon B (PROPx (P) (LOCALx Q (SEPx (R1::R)))).