Your math teacher is weird. But you can just turn it around:

c < 1

c < x/x | •x

xc < x q.e.d.

This also shows, that c≥0 is not actually a requirement, but x>0 is

I guess if your math teacher is completely insufferable, you need to add the definitions of the arithmetic operations but at that point you should also need to introduce Latin letters and Arabic numerals.