(* similar remark apply here… *)

(*****************************************************************************)
(*                                                                           *)
(*                 Fetching the correct info in various cases                *)
(*                                                                           *)
(*****************************************************************************)
Lemma get_info_in_list trs bcl st f:
let trsl:=snd (lm_to_ml (map BC_to_TRS bcl) st) in
trs ∈ trsl → f ∈ all_lhs_funcs trs →
get_info_l trsl f = get_info trs f.