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Let [itex]A,A', B, B'[/itex] be four real numbers, each in the range [itex][0,1][/itex]. Show that:

[itex]AB + AB' + A'B \leq A' B' + A + B[/itex]

(or show a counter-example, if it's not true)

This inequality was inspired by Bell's Theorem, but that's not relevant to proving or disproving it.