(* similar remark apply here… *)

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(*                                                                           *)
(*     fun in rhs are defined somewhere (ie, in at least one lhs)            *)
(*                                                                           *)
(*****************************************************************************)
(* main is defined *)
Lemma BC_to_TRS_main_defined bc st:
let trs := snd (BC_to_TRS bc st) in
trs.(main) ∈ all_lhs_funcs trs.