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07/30/07 7:11pm

I have the following program to run in Mathematica:

Reduce[Reduce[{Mod[x, Abs[a]] == Mod[xP, Abs[a]], (xP < a), Exists[{xPP}, ! (xPP < a) && xP == xPP - a]}], {xP}]

Mathematica uses the Exist equations and the inequalities to arrive at the fact that 0<xP<a. At this point, I would like Mathematica to realize that if 0<xP<a, then Mod[xP,Abs[a]]=xP, and that the final solution should be that xP == Mod[x, Abs[a]].

I have tried various methods such as If statements, and none of it reaches this solution.

Reduce[{Mod[x, Abs[a]] == Mod[xP, Abs[a]], 0<xP<a},xP] also does not work, no simplification is found.

Why is Mathematica unable to reach this conclusion in this method, and how can I make it reach this conclusion?

I would appreciate any advice.

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