intros.
pols.
auto.
Qed.

(* Specifications: *)
Theorem pols_test5:
forall x y z, x + y * (y + z) = 2 * z ->  2 * x + y * (y + z) = (x + z) + z.
Theorem polf_test1: forall x y, (1 <= y -> x  <= x  * y).
intros.
Theorem pols_test5:
forall x y z, x + y * (y + z) = 2 * z ->  2 * x + y * (y + z) = (x + z) + z.
Theorem polf_test1: forall x y, (1 <= y -> x  <= x  * y).
intros.
Theorem pols_test5:
forall x y z, x + y * (y + z) = 2 * z ->  2 * x + y * (y + z) = (x + z) + z.
Theorem polf_test1: forall x y, (0 <= x -> 1 <= y -> x  <= x  * y)%Z.
intros.
Theorem pols_test5:
forall (x y z : R),
x * (z + 2) < y * (2 * x + 1)->  (x * ((z + y) + 2) < y * (3 * x + 1)).
Theorem polf_test1: forall x y, (0 <= x -> 1 <= y -> x  <=  x  * y)%R.
intros.