theorem Th51:
  for W ex T st W + T = ID(M)
proof
  let W;
  reconsider x = W as Vector of M by Th48;
  consider y being Vector of M such that
A1: x + y = ID(M) by Th45;
  reconsider T = y as Element of setvect(M) by Th48;
  x + y = W + T by Def13;
  hence thesis by A1;
end;
