Definition orp_witnessed: context -> Prop :=
  fun Phi => forall x y, Phi (orp x y) -> Phi x \/ Phi y.Definition context_orp_captured (P: context -> Prop): Prop :=
  forall Phi Psi, P (context_orp Phi Psi) -> P Phi \/ P Psi.

Lemma context_orp_mono: forall Phi Psi Phi' Psi', Included _ (derivable Phi) (derivable Phi') -> Included _ (derivable Psi) (derivable Psi') -> Included _ (context_orp Phi Psi) (context_orp Phi' Psi').