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 subst_env_Update: forall rho e1 e2 e3, subst_env rho (Update e1 e2 e3) = Update (subst_env rho e1) (subst_env rho e2) (subst_env rho e3).