Local Open Scope logic_base.
Section ContextProperty.
Context {L: Language}.
Definition at_least (P cP: context -> Prop): Prop :=
forall (Phi: context), cP Phi -> P Phi.

Lemma at_least_left: forall P cP1 cP2, at_least P cP1 -> at_least P (Intersection _ cP1 cP2).