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Assumptions sometimes work as expected with Piecewise, for example

 Simplify[Piecewise[{{A, a + b >= c}, {B, True}}], Assumptions -> a + b > c]

correctly yields the symbol A.

But sometimes they do not work as expected, for example

 Simplify[Piecewise[{{A, a b + c d >= e f}, {B, True}}], Assumptions -> a b + c d > e f]

yields a Piecewise expression with both pieces even though the Assumptions clearly preclude B. Is there some way to help Simplify along in cases like this?

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    $\begingroup$ Has nothing to do with Piecewise. The first works because Simplify[a + b >= c, a + b > c] returns True, while the second fails because Simplify[a b + c d >= e f, a b + c d > e f] returns unsimplified. $\endgroup$
    – Carl Woll
    Commented Jul 28, 2021 at 19:42

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