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

theorem Th3:
  for X being RealNormSpace, x being Point of X holds
  (for e being Real st e > 0 holds ||.x.|| < e) implies x = 0.X
  proof
    let X be RealNormSpace, x be Point of X;
    assume
A1: for e being Real st e > 0 holds ||.x.|| < e;
    assume x <> 0.X;
    then 0 <> ||.x.|| by NORMSP_0:def 5;
    hence contradiction by A1;
  end;
