proposition: Lemma inductive_sat_om (rho : nat -> V) : (ω .: rho) ⊨ is_inductive $0.
proof: Proof. Proof using VIEQ M_ZF. cbn. setoid_rewrite VIEQ. 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.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets(minZF ZF) Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_ZF Undecidability(Shared.ListAutomation)