proposition: Lemma combinations_subst B x y sigma : (combinations B x y)[sigma] = combinations B x`[sigma] y`[sigma].
proof: Proof. induction B as [|[s t] B IH] in sigma, x, y |- *. - cbn. reflexivity. - cbn -[is_rep]. rewrite IH, is_rep_subst. cbn -[is_rep]. now subsimpl. Qed.
imports: Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Deduction.FullNDFacts Undecidability.FOL.Sets.FST Undecidability.FOL.FST Undecidability.FOL.Reductions.PCPb_to_FST Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)