I was coding up some bounds propagation in some constraint satisfaction code I was playing with and decided to see if Mathematica could simplify an expression involving Min and Max. I extracted the essence of what it seemed not to be able to do.
FullSimplify[Max[a, Max[b, c]]]
gives what I expect:
Max[a, b, c]
FullSimplify[Max[a, Max[b + z, c + z] - z]]
Max[a, -z + Max[b + z, c + z]]
Often though Mathematica knows more than me. Am I missing something here?