proposition: Lemma Incl_M_R_unfolded_auxiliary_61: forall (a b c d:Q), 0 < d + c -> (d+c)*((a+b)*(-1/2+(2+1)/2))<=(d+c)*((c+d)*(1/2+1/2))-> (a + b) / (c + d) <= 1.
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_pos_l _ _ _ Hdc H0); clear H0; replace (-1/2 + (2+1)/2) with Qone; [|qZ_numerals; field; auto]; replace (1/2 + 1/2) with Qone; [|qZ_numerals; field; auto]; intros H_mult; assert (Hcd:Zero<c+d);[ring_exact_Q Hdc|]; apply Qmult_pos_Qdiv_Qle; trivial; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M