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 m e1 e2 e3, subst_env' m rho (Update e1 e2 e3) = Update (subst_env' m rho e1) (subst_env' m rho e2) (subst_env' m rho e3).