
theorem
  for V being RealUnitarySpace, W being Subspace of V, L being
  Linear_Compl of W holds W is Linear_Compl of L
proof
  let V be RealUnitarySpace, W be Subspace of V, L be Linear_Compl of W;
  V is_the_direct_sum_of L,W by Def5;
  then V is_the_direct_sum_of W,L by Lm15;
  hence thesis by Def5;
end;
