(* fetching rhs functions names *)
Definition rhs_funcs ru :=  (* => Syntax.v ? *)
  match ru with
  | rule_intro _ _ t => functions_of_term t
  end.Definition all_rhs_funcs prg := flat_map rhs_funcs prg.

Lemma get_info_main_eq trs: match assoc Nat.eqb trs.(main) trs.(infos) with | Some inf => inf | None => Err_info end = get_info trs trs.(main).