Definition maximal (P: context -> Prop): context -> Prop :=
  fun Phi => P Phi /\ forall Psi, P Psi -> Included _ Phi Psi -> Included _ Psi Phi.

Lemma sig_context_ext: forall (cP: context -> Prop) (Phi Psi: sig cP), (forall x, proj1_sig Phi x <-> proj1_sig Psi x) -> Phi = Psi.