proposition: Lemma prv_to_min_sym { p : peirce } : binZF ⊢ rm_const_fm ax_sym.
proof: Proof. prv_all' x. prv_all' y. subsimpl. apply II. assert1 H. use_exists' H a. assert1 H'. apply CE2 in H'. use_exists' H' b. repeat simpl_ex. eapply minZF_trans; auto. - apply minZF_sym; auto. eapply CE1. auto. - eapply minZF_trans; auto. apply minZF_sym; auto. eapply CE2. auto. eapply CE1, Ctx. auto. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Syntax.Asimpl Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets(binZF ZF) Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability(Shared.ListAutomation) Morphisms Undecidability.FOL(Reductions.PCPb_to_ZFeq)