Tactic Notation "rewr" constr(e) := match goal with E : e = _ |- _ => rewrite E | E : _ = e |- _ => rewrite <-E end.
Tactic Notation "rewr" constr(e) "in" "*" := match goal with E : e = _ |- _ => rewrite E in * | E : _ = e |- _ => rewrite <-E in * end.
Tactic Notation "rewr" constr(e) "in" hyp(H) := match goal with E : e = _ |- _ => rewrite E in H | E : _ = e |- _ => rewrite <-E in H end.
(* Subject reduction : taking a step let us stay in the invariant *)
Variable sameperms_corestep : forall c m c' m', corestep c m c' m' -> sameperms m m'.

Theorem subject_reduction x y : x ===> y -> P x -> P y.