Definition cP : context -> Prop := Intersection _ (Intersection _ derivable_closed orp_witnessed) consistent.

(* Specifications: *)
Lemma AL_DC: at_least derivable_closed cP.
Lemma AL_OW: at_least orp_witnessed cP.
Lemma AL_CONSI: at_least consistent cP.
Lemma LIN_CD: forall x: expr, Lindenbaum_constructable (cannot_derive x) cP.
Lemma LIN_SL: forall (Phi: context) (Psi: sig cP), Lindenbaum_constructable (context_sepcon_included_l Phi (proj1_sig Psi)) cP.
Lemma LIN_SR: forall (Phi: context) (Psi: sig cP), Lindenbaum_constructable (context_sepcon_included_r Phi (proj1_sig Psi)) cP.
Lemma AL_DC: at_least derivable_closed cP.
Lemma AL_OW: at_least orp_witnessed cP.
Lemma AL_CONSI: at_least consistent cP.
Lemma LIN_CD: forall x: expr, Lindenbaum_constructable (cannot_derive x) cP.