reserve n for non zero Element of NAT;
reserve a,b,r,t for Real;

theorem
  for X being RealNormSpace, x,y being Point of X holds
  (for e being Real st e > 0 holds ||.x-y.|| < e) implies x = y
proof
  let X be RealNormSpace, x,y be Point of X;
  assume for e being Real st e > 0 holds ||.x-y.|| <e;
  then x-y = 0.X by Th3;
  hence thesis by RLVECT_1:21;
end;
