
theorem Lm72:
for V be RealNormSpace, x be Point of V st
 for f be Lipschitzian linear-Functional of V holds f.x = 0
  holds x = 0.V
proof
   let V be RealNormSpace, x be Point of V;
   assume AS: for f be Lipschitzian linear-Functional of V holds f.x = 0;
   assume x <> 0.V; then
   ex G be Point of DualSp V st
    (Bound2Lipschitz(G,V)).x = 1 & ||.G.|| = 1/||.x.|| by Lm65a;
   hence contradiction by AS;
end;
