proposition: Lemma Incl_M_M_unfolded_auxiliary_62: forall (a b c d:Q), d + c<0 -> (d+c)*((a+b)*(0 / 1 + (2 + 1) / 1))<=(d+c)*((c+d)*(1 / 1 + 0 / 1))-> (a + b) / (c + d) <= 1/3.
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_neg_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; assert (Hcd:c+d<Zero);[ring_exact_Q Hdc|]. apply Qmult_Qdiv_neg_pos_Qle; auto; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M