proposition: Lemma Qlt_shift_div_l : forall a b c, 0 < c -> a*c < b -> a < b/c.
proof: Proof. intros a b c Hc H. apply Qnot_le_lt. intros H0. apply (Qlt_not_le _ _ H). apply Qmult_lt_0_le_reg_r with (/c). - apply Qinv_lt_0_compat. assumption. - setoid_replace (a*c/c) with (a) by (apply Qdiv_mult_l; auto with *). assumption. Qed.
imports: ZArith_base ZArithRing ZArith.BinInt Morphisms Setoid Bool