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 Th1: :: EUCLID:31
  0 * x + x = x & x + 0*n = x
proof
  reconsider x9 = x as Element of n-tuples_on REAL;
  0 *x + x = 0 *x9 + 1*x9 by RVSUM_1:52
    .= (0+1)*x9 by RVSUM_1:50
    .= x by RVSUM_1:52;
  hence thesis by RVSUM_1:16;
end;
