proposition: Lemma Incl_M_M_unfolded_auxiliary_51: forall (a b c d:Q), 0 < d - c -> (d-c)*((d-c)*(0/1-1/1))<=(d-c)*((b-a)*((2+1)/1- 0/1))-> (-1)/3 <= (b - a) / (d - c).
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_pos_l _ _ _ Hdc H0); clear H0; replace (0/1 - 1/1) with (Qopp Qone); [|qZ_numerals; field; auto]; replace ((2+1)/1 - 0/1) 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