
theorem Th37:
  for V being RealUnitarySpace, W being Subspace of V, L being
  Linear_Compl of W holds W /\ L = (0).V & L /\ W = (0).V
proof
  let V be RealUnitarySpace, W be Subspace of V, L be Linear_Compl of W;
  V is_the_direct_sum_of W,L by Th35;
  hence W /\ L = (0).V;
  hence thesis by Th14;
end;
