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(* GNU General Public License for more details.                       *)
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(* 02110-1301 USA                                                     *)
Require Export Qpositive_order.
Definition Qpositive_sub (w w' : Qpositive) :=
let (p, q) := Qpositive_i w in
let (p', q') := Qpositive_i w' in
Qpositive_c (p * q' - p' * q) (q * q') (p * q' + p' * q + q * q').

Theorem lt_mult_conv : forall x y z : nat, S x * y < S x * z -> y < z.
intros x y z.