proposition: Lemma subst_cast {b} sigma phi : cast (subst_form sigma phi) = subst_form sigma (cast phi).
proof: Proof. induction phi in sigma |- *; cbn in *; trivial. - destruct b0. cbn. congruence. - destruct q. cbn. congruence. 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.FOL.Reductions.PCPb_to_FOL Undecidability.PCP.Reductions.PCPb_iff_dPCPb List Undecidability(Shared.ListAutomation)