proposition: Lemma Incl_M_L_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)<=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; apply Qmult_resp_Qle_pos_l with 2; auto; rewrite Qdiv_Qmult_numerator_l; auto; apply Qmult_neg_Qdiv_Qle; trivial; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M