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Simplification with custom axioms


Hi all,

I wonder if it's possible to get Mathematica to understand specified
properties of functions when simplifying.
For example, by default it does not know that BitAnd[x, y] <= x:

In = FullSimplify[BitAnd[x, 10] <= 10]
Out = BitAnd[10, x] <= 10
(expected result is True)

I tried using ForAll, but without success:

In = Assuming[
  ForAll[{x, y}, 0 <= BitAnd[x, y] <= x && 0 <= BitAnd[x, y] <= y],
  FullSimplify[BitAnd[10, x] <= 10]]
Out = BitAnd[10, x] <= 10

Any ideas?


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