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_consistent_rev_left: forall (Phi1 Phi2 Psi: context), Included _ (context_sepcon Phi1 Phi2) Psi -> consistent Psi -> consistent Phi1.