theorem
  for L being Linear_Compl of W, v being Element of V, t being Element
  of [:the carrier of V,the carrier of V:] holds t`1 + t`2 = v & t`1 in W & t`2
  in L implies t = v |-- (W,L)
proof
  let L be Linear_Compl of W;
  let v be Element of V;
  let t be Element of [:the carrier of V,the carrier of V:];
  V is_the_direct_sum_of W,L by Th38;
  hence thesis by Def6;
end;
