Definition Qmult_resp_Qlt_pos_l:= Qlt_Qmult_cancel_l: forall t x y : Q, Zero < t -> t * x < t * y -> x < y.

Lemma Qmult_Qlt_Qle_pos_nonneg_compat: forall n m p q, n <= p -> m < q -> Zero < p -> Zero <= m -> n * m < p * q.
Ltac qZ_numerals_one  :=replace (Z_to_Q 1) with Qone;  trivial.