Definition context_sepcon_included_l (Phi2 Psi: context): context -> Prop :=
  fun Phi1 => Included _ (context_sepcon Phi1 Phi2) Psi.Definition context_sepcon_included_r (Phi1 Psi: context): context -> Prop :=
  fun Phi2 => Included _ (context_sepcon Phi1 Phi2) Psi.

Lemma context_sepcon_included_equiv: forall Phi Psi, derivable_closed Psi -> Same_set _ (context_sepcon_included_l Phi Psi) (context_sepcon_included_r Phi Psi).