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

forall x in Z, y in Z: 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)

Author: Wolfgang Schreiner
Last Modification: November 16, 1999

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