proposition: Lemma existSys (T : System) (f g : Formula) (v : nat): ~ In_freeVarSys LNT v T -> ~ In v (freeVarF g) -> SysPrf (Ensembles.Add _ T f) g -> SysPrf (Ensembles.Add _ T (exH v, f)%nt) g.
proof: Proof. apply (existSys LNT). Qed.
imports: Coq(Arith Ensembles List) hydras.Ackermann(Languages folProof folProp folLogic3)