proposition: Lemma nat_H10 E : (forall rho, sat interp_nat rho (embed E)) -> H10p E.
proof: Proof. destruct E as [a b]. unfold embed in *. intros H. specialize (H (fun _ => 0)). apply subst_exist_sat2 in H as [sigma H]. exists sigma. unfold H10p.H10p_sem. cbn. rewrite <- !nat_eval_poly. apply H. Qed.
imports: Undecidability.Synthetic.Definitions Undecidability.FOL(Syntax.Facts Deduction.FullNDFacts Semantics.Tarski.FullFacts Semantics.Tarski.FullSoundness) Undecidability.FOL.PA Undecidability.FOL.Arithmetics(TarskiFacts DeductionFacts NatModel) Undecidability.H10(H10p) List Lia