proposition: Lemma Incl_M_M_unfolded_auxiliary_72: forall (a b c d:Q), d+c<0 -> (d+c)*((c+d)*(0 / 1 - 1 / 1))<=(d+c)*((a+b)*((2 + 1) / 1 - 0 / 1)) -> (-1)/3 <= (a + b) / (c + d).
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_neg_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; assert (Hcd:c+d<Zero);[ring_exact_Q Hdc|]; apply Qmult_Qdiv_pos_neg_Qle; auto; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M