proposition: Lemma reduceAddExists : forall (n m : nat) (A B : Formula), SysPrf NN (iffH A B) -> SysPrf NN (iffH (addExists m n A) (addExists m n B)).
proof: Proof. intros n m A B H. induction n as [| n Hrecn]; simpl in |- *; auto. apply (reduceExist LNN); auto. apply closedNN. Qed.
imports: Coq(Arith) hydras.Ackermann(extEqualNat subAll folProp subProp folReplace folLogic3 NN NNtheory primRec expressible) Coqprime(ChineseRem) Coq(Vector List Lia) hydras(ListExt cPair MoreDecidable) hydras(Compat815 ssrnat_extracts) Coq(Utf8)