theorem
  for L being Linear_Compl of W, v being Element of V holds (v |-- (W,L)
  )`1 in W & (v |-- (W,L))`2 in L
proof
  let L be Linear_Compl of W;
  let v be Element of V;
  V is_the_direct_sum_of W,L by Th38;
  hence thesis by Def6;
end;
