theorem Th52:
  for W,W1,W2 st W + W1 = ID(M) & W + W2 = ID(M) holds W1 = W2
proof
  let W,W1,W2 such that
A1: W + W1 = ID(M) & W + W2 = ID(M);
  reconsider x = W,y1 = W1,y2 = W2 as Vector of M by Th48;
  x + y1 = W + W2 by A1,Def13
    .= x + y2 by Def13;
  hence thesis by Th47;
end;
