proposition: Lemma Is_refining_T_product_hd:forall xi alpha beta, Is_refining_T xi -> Is_refining_T (right_product (left_product xi (map_digits (hd alpha))) (map_digits (hd beta))).
proof: Proof. intros xi [[ | | ] alpha] [[ | | ] beta] H_xi; unfold hd; apply Is_refining_T_left_right_product; trivial; first [apply Is_refining_M_L|apply Is_refining_M_R|apply Is_refining_M_M]. Qed.
imports: digits Refining_M Bounded_T QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Fourier