proposition: Lemma Z_decomp { p : peirce } phi : Zeq ⊢T phi -> exists A, (map ax_sep A ++ ZFeq') ⊢ phi.
proof: Proof. intros [A [H1 H2]]. induction A in phi, H1, H2 |- *. - exists nil. cbn. eapply Weak; eauto. - rewrite <- imps in H2. apply IHA in H2 as [B H]; auto. rewrite imps in H. destruct (H1 a); auto. + exists B. eapply Weak; try apply H. auto. + exists (phi0 :: B). cbn. apply H. Qed.
imports: Undecidability.FOL(Semantics.Tarski.FullFacts Syntax.Facts Deduction.FullNDFacts) Undecidability.FOL.Sets(ZF minZF) Undecidability.FOL.Reductions(PCPb_to_ZF PCPb_to_minZF PCPb_to_ZFD) Undecidability(Shared.ListAutomation)