proposition: Lemma standard_embed_problem' E rho f : extensional I -> (forall d, iμ (f d) = d) -> (forall n, f (iμ n) = n) -> rho ⊨ embed_problem E -> H10p_sem E (rho >> f).
proof: Proof. Proof using FA_model. intros HI Hf1 Hf2 H. destruct E as [p q]. apply HI in H. unfold H10p_sem. cbn. rewrite <- Hf2 at 1. setoid_rewrite <- Hf2 at 3. f_equal. now rewrite <- !standard_embed_poly. 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