proposition: Lemma nOr (T : System) (f g : Formula): SysPrf T (~ f /\ ~ g)%fol -> SysPrf T (~ (f \/ g))%fol.
proof: Proof. intros H; apply absurd1, impI, orSys. - apply contradiction with f. + apply Axm; right; constructor. + apply sysWeaken; eapply andE1; apply H. - apply contradiction with g. + apply Axm; right; constructor. + apply sysWeaken; eapply andE2; apply H. Qed.
imports: Coq(Ensembles List) hydras.Ackermann(ListExt folProof folProp Deduction)