proposition: Lemma IB_eval_Some rho t u v : eval rho t = Some v -> eval rho (prep u t) = Some (u ++ v).
proof: Proof. intros H. induction u; cbn; trivial. unfold prep in IHu. fold prep in IHu. now rewrite IHu. Qed.
imports: Undecidability.PCP(PCP Util.PCP_facts) Undecidability.FOL(Deduction.FragmentNDFacts Semantics.Tarski.FragmentFacts Semantics.Tarski.FragmentSoundness Syntax.Core Syntax.Facts) Undecidability.FOL(FOL) Undecidability.Synthetic(Definitions DecidabilityFacts EnumerabilityFacts ReducibilityFacts MoreReducibilityFacts) Undecidability.PCP.Reductions.PCPb_iff_dPCPb Undecidability(Shared.ListAutomation)