proposition: Lemma existSys (T : System) (f g : Formula) (v : nat): ~ In_freeVarSys LNN v T -> ~ In v (freeVarF g) -> SysPrf (SetAdds T f) g -> SysPrf (SetAdds T (exH v, f)%fol) g.
proof: Proof. apply (existSys LNN). Qed.
imports: Coq(Arith Ensembles List) LibHyps(LibHyps) hydras(MoreLibHyps NewNotations)