(* similar remark apply here… *)

Lemma map_BC_to_TRS_func_bounds bcl st f:
let lm := map BC_to_TRS bcl in
let trsl := snd ((lm_to_ml lm) st) in
let lst := fst ((lm_to_ml lm) st) in
f ∈ flat_map all_lhs_funcs trsl → st+1 ≤ f ≤ lst.