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how implement a rule


I want to define a function abs (mimicking Abs) with various properties. 
One part of the definition is:

   abs[c_ z_ /; c \[Element] Reals] = Abs[c] abs[z]

Given that, how might I express that abs[z] is always real in such a way 
that the result of

   abs[1/abs[z]^2]

will be 1/abs[z]^2 -- WITHOUT explicitly introducing, say:

   abs/: abs[1/abs[z_]^2] =  1/abs[z]^2

?

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
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University of Massachusetts                413 545-2859 (W)
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Amherst, MA 01003-9305


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