proposition: Lemma enc_stack_app T B C : HFeq <<= T -> T ⊢ (enc_stack B) ∪ (enc_stack C) ≡ enc_stack (B ++ C).
proof: Proof. intros HT. induction B as [|[s t] B IH]; cbn. - eapply Weak; try apply bunion_eset. assumption. - eapply HF_trans'; trivial. eapply Weak; try apply bunion_swap; trivial. eapply HF_eq_bunion; trivial. apply HF_refl'; trivial. Qed.
imports: Undecidability.FOL.ZF Undecidability.FOL.Syntax.Facts Undecidability.FOL.Semantics.Tarski.FullFacts Undecidability.FOL.Sets.ZF Undecidability.FOL.Reductions.PCPb_to_HF Undecidability.PCP(PCP Util.PCP_facts Reductions.PCPb_iff_dPCPb) Undecidability(Shared.ListAutomation)