(* similar remark apply here… *)

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(*                                                                           *)
(*     the list of fun having an info is exactly the list of fun in lhs      *)
(*                                                                           *)
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Lemma BC_to_TRS_all_funs_have_info bc st f:
let trs := snd (BC_to_TRS bc st) in
f ∈ all_lhs_funcs trs → f ∈ map fst trs.(infos).