proposition: Lemma nf_pred a: T3nf a -> T3nf (T3pred a).
proof: Proof. elim:a => // a _ b _ c _ n d Hd /= /and5P [pa pb pc /Hd pd pe]. case az: (all_zero a b c); first by apply: nf_finite. by rewrite /= pa pb pc pd /= (T3le_lt_trans (pred_le d) pe). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(fintype bigop)