proposition: Lemma IB_sNot rho f : rho ⊨ (f → sFalse) <-> ((rho ⊨ f) -> H10UPC_SAT h10).
proof: Proof. split. * intros H. cbn in H. now rewrite IB_sFalse in H. * intros H. cbn. now rewrite IB_sFalse. Qed.
imports: Undecidability.DiophantineConstraints(H10C) Undecidability.DiophantineConstraints.Util(H10UPC_facts) Undecidability.FOL(Utils.FriedmanTranslationFragment 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) Coq(Arith Lia List) Undecidability.FOL.Reductions(H10UPC_to_FOL_constructions)