Hint Resolve mprod_hom.
Definition is_decomposable n M := exists l, decomposable n l M.

Lemma decomposable_factor n k x M : x <> 0 -> hom n 1 x -> hom n k.+2 M ->
is_decomposable n M -> x ∨ M = 0 -> is_decomposable n (factor n x M).