Here is my problem: I have several variables that I know are unknown and have arbitrary values. Let's call them C[1], C[2], and C[3]. After doing some magic with Solve[ ... ] and Reduce[ ... ] and Simplify[ ... ], I get the expression:

C[1]+C[2]+C[3]

Now, I know two things about these variables: they have arbitrary values, but each variable is an integer. So C[1] spans Z, C[2] spans Z, etc. Therefore, their sum spans Z. This is quite obvious. Mathematica gives me a conditional expression like

ConditionalExpression[C[1]+C[2]+C[3],C[1] is in Integers && C[2] is in Integers && C[3] is in Integers]

Which is swell, but I know their sum is also an arbitrary integer. How would I tell Mathematica to replace C[1]+C[2]+C[3] with C[4], C[4] is in integers? Or to do this for arbitrary sums of unknowns, where the properties of the result are obvious but somewhat hard to read in their full form.

Thanks!