reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;

theorem
  x1 <> x2 implies |.x1 - x2.| > 0
proof
  assume x1 <> x2;
  then 0 <> |.x1 - x2.| by Th13;
  hence thesis;
end;
