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_l_finite_captured: forall Phi2 Psi, finite_captured (context_sepcon_included_l Phi2 Psi).