Definition HLIP_sound_aux2 (hd: expr typ func): rtac_sound (solve_hd_in_hlip hd) :=
    match hd as hd'
      return rtac_sound match hd' with
                        | App (Inj (inr (Smx flater))) _ => EAPPLY typ func reify_derives_refl
                        | _ => EAPPLY typ func reify_now_later
                        end
    with
    | App (Inj (inr (Smx flater))) _ => APPLY_sound_derives_refl tbl
    | _ => APPLY_sound_now_later tbl
    end.

(* Specifications: *)
Lemma HLIP_sound: forall temp var ret gt R s, rtac_sound (HLIP temp var ret gt R s).