Fusion law for foldr1?

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For foldr we have the fusion law: if f is strict, f a = b, and

f (g x y) = h x (f y) for all x, y, then f . foldr g a = foldr h b.

How can one discover/derive a similar law for foldr1? (It clearly can't even take the same form - consider the case when both sides act on [x].)

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