= Solution
For a \b[finite outer <list>] of <proper lazy lists>, use the fair binary product from part f:
``
cp :: [[a]] -> [[a]]
cp [] = [[]]
cp (xs:xss) = fairPair (:) xs (cp xss)
``
The empty family has one selection, the empty selection. For a nonempty finite family, each selection consists uniquely of one first-factor occurrence followed by a selection from the remaining factors. <Induction> on the number of factors, together with the fairness of `fairPair`, proves that every such selection is produced and no invalid selection is introduced. Infinite factors are allowed: in particular, the three-factor example is enumerated fairly. If any factor is empty, the finite-family computation returns the empty product.
The printed hypothesis also permits an \i[infinite outer] <proper lazy list>. \b[No <function> can satisfy the full enumeration requirement for all such inputs.] Take `repeat [0,1]`. Its mathematical <Cartesian product> contains every infinite binary sequence and is <uncountable>. If a result <list> enumerated these sequences as $z_0,z_1,\ldots$, the binary sequence $b$ with $b_i=1-z_i(i)$ would differ from the $i$-th listed sequence at position $i$, contradicting completeness. This is an <uncountability obstruction to enumerating infinite Cartesian products>. The finite-outer qualification is a necessary repair to the specification, not a restriction imposed for convenience by the code.
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