The empty family has one choice, the empty selection:
cp :: [[a]] -> [[a]]
cp = foldr extend [[]]
  where
    extend choices suffixes = [x:ys | x <- choices, ys <- suffixes]
A selection from the whole family consists uniquely of a choice from its first member and a selection from the remaining family. This bijection proves the combining equation and completeness by induction. If a member family is empty, there are no selections. The base is [[]], not []: otherwise every Cartesian product would incorrectly be empty.

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