Hello there.

I need to write a following formula using quantifiers, but it has to be in prenex normal form.

The formula is : function f is not weakly decreasing and not weakly increasing.

I got to here:

$\displaystyle \exists x \exists y(x \le y \wedge f(x)>f(y)) \wedge \exists x\exists y(x \le y \wedge f(x)<f(y))$

by negating :

$\displaystyle (\forall x \forall y(x \le y \wedge f(x)\le f(y)) \vee (\forall x \forall y(x \le y \wedge f(x)\le f(y)) $

But I have no idea how to proceed, since my solution is not in prenex normal form.

Please help.