proposition: Lemma cp2 (T : System) (f g : Formula): SysPrf T (g -> f)%fol -> SysPrf T (~f -> ~g)%fol.
proof: Proof. intros H; apply impE with (~ ~ g -> ~ ~ f)%fol. - exists (nil (A:=Formula)). exists (CP L (~ g)%fol (~ f)%fol); contradiction. - apply impI, nnI; apply impE with g. + apply sysWeaken; assumption. + apply nnE, Axm; right; constructor. Qed.
imports: Coq(Ensembles List) hydras.Ackermann(ListExt folProof folProp Deduction)