proposition: Lemma Incl_M_L_unfolded_auxiliary_62: forall (a b c d:Q), d+c<0 -> (d+c)*((a+b)*(1/2+(2+1)/2))<=(d+c)*((c+d)*(1/2+-1/2))-> (a + b) / (c + d) <= 0.
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_neg_l _ _ _ Hdc H0); clear H0; replace (1/2 + (2+1)/2) with (Qone +Qone); [|qZ_numerals; field; auto]; replace (1/2 + -1/2) with Zero; [|qZ_numerals; field; auto]; repeat rewrite Qmult_zero_right; intros H_mult; assert (Hcd:c+d<Zero);[ring_exact_Q Hdc|]; apply Qle_Qdiv_nonneg_neg; trivial; apply Qmult_resp_Qle_pos_l with 2; auto; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M