reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem Th3: :: EUCLID:33
  1*x = x & 0 * x = 0*n
proof
  reconsider x9 = x as Element of n-tuples_on REAL;
  (0)*x = (0)*x9 + x9 - x9 by RVSUM_1:42
    .= x9 - x9 by Th1
    .= 0*n by RVSUM_1:37;
  hence thesis by RVSUM_1:52;
end;
