4.1 Old friend

Let us explore the following proposition (that is improper):

$(x < y) \rightarrow (x \le y)$

It was improper because x and y are not bound. Now that we know about the ``for all'' and ``there exist'' concepts, we can bind x and y properly. Let I represent the set of integers, then we can write the following:

$\forall x \in \mathrm{I}:(\forall y \in \mathrm{I}:(x < y) \rightarrow (x \le y))$