proposition: Theorem H10p_to_PA_prv E : H10p E <-> PAeq ⊢TI embed E.
proof: Proof. split. - intros [sigma HE]. exists FAeq. split. intros. now constructor. apply H10p_to_FA_prv. now exists sigma. - intros H. apply nat_sat'. eapply subst_exist_sat2. eapply (tsoundness H (rho:=id)). intros. now apply nat_is_PAeq_model. 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