proposition: Lemma Incl_M_L_unfolded_auxiliary_52: forall (a b c d:Q), d - c<0 -> (d-c)*((d - c) * (-1 / 2 - 1 / 2)) <= (d-c)*((b - a) * ((2 + 1) / 2 - 1 / 2)) -> -1 <= (b - a) / (d - c).
proof: Proof. intros a b c d Hdc H0; generalize (Qmult_resp_Qle_neg_l _ _ _ Hdc H0); clear H0; replace (-1/2 - 1/2) with (Qopp Qone); [|qZ_numerals; field; auto]; replace ((2+1)/2 - 1/2) with Qone; [|qZ_numerals; field; auto]; intros H_mult; apply Qmult_neg_Qle_Qdiv; trivial; ring_exact_Q H_mult. Qed.
imports: digits Raxioms RIneq QArithSternBrocot(R_addenda) Fourier_solvable_ineqs Bounded_M