Open Scope N_scope.
intros.
pols.
auto.
Qed.
intros.
pols.
auto.
Qed.
intros.
pols.
auto.
Qed.
intros.
pols.
auto.
Qed.
intros.
polf.
Qed.

Theorem polf_test2: forall x y, 0 < x -> x  <= x  * y -> 1 <= y.