This is in continuation of Origamic II.

A sheet of paper has the exact shape of a rectangle (denoted by ABCD) where the length of AB is greater than or equal to the length of AD. The vertex A is folded onto the vertex C, resulting in the crease EF (E on AB and F on CD).

The paper is thereafter unfolded and, the vertex A is folded onto F so that, the length of the resulting crease is equal to AB.

Is ABCD always a square? If so, prove it - otherwise, give a counter example.