theorem Th40:
  for L being Linear_Compl of W holds W /\ L = (0).V & L /\ W = (0).V
proof
  let L be Linear_Compl of W;
A1: V is_the_direct_sum_of W,L by Th38;
  hence W /\ L = (0).V;
  thus thesis by A1;
end;
