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*Proposition:*
For every integer `x` and `y` the difference is defined:

forallxinZ,yinZ:x= (x-y)+y.

*Proof:*
Take arbitrary `x` in **Z** and `y` in **Z**. We have

( x-y)+y= (definition of -) ( x+(-y))+y= (associativity of +) x+((-y+y))= (*) x+0= (definition of + and 0) x.

Author: Wolfgang Schreiner

Last Modification: November 16, 1999