proposition: Lemma Incl_M_R_unfolded_auxiliary_82: forall (a b c d:Q), d-c<0 -> (d-c)*((b-a)*(-1 / 2 + (2 + 1) / 2))<=(d-c)*((d-c)*(1 / 2 + 1 / 2)) -> (b - a) / (d - c)<=1.
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; [|qZ_numerals; field; auto]; replace (1/2 + 1/2) with Qone; [|qZ_numerals; field; auto]; intros H_mult; apply Qmult_neg_Qdiv_Qle; trivial; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M