(* similar remark apply here… *)

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(*                                                                           *)
(*                       Max arity is correct                                *)
(*                                                                           *)
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Lemma max_arity_prog_cons (r:rule) rl: (* => Syntax.v ? *)
max_arity_prog (r::rl) =
max (max_arity_rule r) (max_arity_prog rl).