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*Proposition:*
Let `a` and `a`' be in the same residue
class and also `b` and `b`' be in the same
residue class. The result of any integer operation involving `a` and
`b` is in the same residue class as if the operation
were performed with `a`' and `b`' instead:

forallminZ_{>0},ainZ,a' inZ,binZ,b' inZ:[ a]_{m}= [a']_{m}/\ [b]_{m}= [b']_{m}=>[ a+b]_{m}= [a'+b']_{m}/\[- a]_{m}= [-a']_{m}/\[ a*b]_{m}= [a'*b']_{m}.

Author: Wolfgang Schreiner

Last Modification: January 12, 2000