proposition: Lemma Incl_M_M_unfolded_auxiliary_81: forall (a b c d:Q), 0<d-c -> (d-c)*((b-a)*(0 / 1 + (2 + 1) / 1))<=(d-c)*((d-c)*(1 / 1 + 0 / 1)) -> (b - a) / (d - c)<=1/3.
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_pos_l _ _ _ Hdc H0); clear H0; replace (1/1 + 0/1) with Qone; [|qZ_numerals; field; auto]; replace (0/1 + (2+1)/1) with (Qone+Qone+Qone); [|qZ_numerals; field; auto]; intros H_mult; apply Qmult_Qdiv_pos_Qle; auto; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M