proposition: Lemma inductive_sat_om (rho : nat -> V) : (ω .: rho) ⊨ is_inductive $0.
proof: Proof. Proof using M_ZF. cbn. setoid_rewrite eq_equiv. split. - exists ∅. split; try apply M_eset; trivial. now apply M_om1. - intros d Hd. exists (σ d). split; try now apply M_om1. intros d'. now apply sigma_el. 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)