# Question: use peano anxiom and properties of nx to prove that...

###### Question details

Use Peano Anxiom and properties of (N,+,x) to prove that if ab=ac and a is nonzero, then b=c, where a,b,c E N.

If a is less than b if and only if b=a+c, and a++<or equal to b (when b=(a++)+d, and d>0.

How do I prove that?