theorem Th37:
  x1,x2 are_lindependent2 implies x1 <> x2
proof
  assume
A1: x1,x2 are_lindependent2;
  assume
A2: x1 = x2;
  1 * x1 + (-1) * x2 = 1 * (x1 - x2) by Th12
    .= 1 * 0*n by A2,Th2
    .= 0*n by EUCLID_4:2;
  hence contradiction by A1;
end;
