proposition: Lemma IB_wFalse rho t : rho ⊨ wFalse t <-> dom_rel (rho t) (rho (S t)).
proof: Proof. split. * intros H. apply H. * intros H. unfold wFalse, Fr. intros P. apply H. apply P. 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)