proposition: Lemma min_embed' (rho : nat -> V) phi : sat I rho (embed' phi) <-> sat min_model' rho phi.
proof: Proof. induction phi in rho |- *; try destruct b0; try destruct q; cbn. 1,3-7: firstorder. destruct P; erewrite Vector.map_map, Vector.map_ext. reflexivity. apply min_embed_eval'. reflexivity. apply min_embed_eval'. Qed.
imports: Undecidability.FOL(Syntax.Facts Semantics.Tarski.FullFacts Deduction.FullNDFacts ZF FST) Undecidability.FOL.Sets(Models.Aczel Models.ZF_model ZF minZF FST) Undecidability.FOL.Reductions(PCPb_to_ZF PCPb_to_ZFeq PCPb_to_minZF PCPb_to_minZFeq PCPb_to_ZFD) Lia Undecidability.PCP(PCP) Undecidability(Shared.ListAutomation)