Ltac show_stopped :=
  let m' := fresh "m'" in
  let e' := fresh "e'" in
  let H := fresh "H" in
  right; intros [m' [e' H]]; inv H.

Lemma stepstar_search : forall f m e m' e', (forall m e m' e', step (m,e) (m',e') -> step (m,f e) (m',f e')) -> stepstar (m,e) (m',e') -> stepstar (m,f e) (m', f e').