\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(E\) be a \(\mathbb{K}\)-vector space and \(F, G, H\) three subspaces of \(E\). Show that the following are equivalent:
  1. \(F\) and \(G\) are in direct sum, and \(F + G\) and \(H\) are in direct sum;
  2. \(F, G, H\) are in direct sum (three-fold).

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