proposition: Lemma IB_N_e rho i n : rho i = n -> rho ⊨ N i -> {m:nat | Num m = n}.
proof: Proof. intros Hrho H. destruct n as [m|a b]. * now exists m. * exfalso. cbn in H. rewrite Hrho in H. apply (@h10_rel_irref (a,b) H). Qed.
imports: Undecidability.DiophantineConstraints(H10C) Undecidability.DiophantineConstraints.Util(H10UPC_facts) Undecidability.FOL(Syntax.Facts Deduction.FragmentNDFacts Semantics.Tarski.FragmentSoundness Semantics.Tarski.FragmentFacts Syntax.BinSig Semantics.Kripke.FragmentCore Semantics.Kripke.FragmentSoundness Semantics.Kripke.FragmentToTarski) Undecidability.Shared(Dec) Undecidability.Shared.Libs.PSL(Numbers) Undecidability.Shared(ListAutomation) Coq(Arith Lia List)