Open Scope R_scope.
intros.
pols.
auto.
Qed.
intros.
pols.
auto.
Qed.
intros.
pols.
auto with real.
Qed.
intros.
pols.
auto.
Qed.
intros.
pols.
auto.
Qed.

Theorem polf_test1: forall x y, (0 <= x -> 1 <= y -> x  <=  x  * y)%R.