
theorem Lm65A:
for V be RealNormSpace st V is non trivial holds
  ex F be Point of DualSp V st ||.F.|| = 1
proof
   let V be RealNormSpace;
   assume V is non trivial; then
   consider x0 be Element of V such that
P1: x0 <> 0.V;
   ex F be Point of DualSp V
    st ||.F.|| = 1 & (Bound2Lipschitz(F,V)).x0 =||.x0.|| by Lm65,P1;
   hence thesis;
end;
