reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;

theorem Th1:
  n is non zero implies x <> x + 1.REAL n
proof
A1: 0.REAL n = 0.TOP-REAL n & x = x + 0.TOP-REAL n by EUCLID:66,RLVECT_1:4;
  assume that
A2: n is non zero and
A3: x = x + 1.REAL n;
   0.REAL n <> 1.REAL n by A2,REVROT_1:19;
  hence thesis by A1,A3,RLVECT_1:8;
end;
