
theorem Th74A:
for X be RealNormSpace st X is non trivial holds
  ex L be Lipschitzian LinearOperator of X, Im(BidualFunc X)
   st L is isomorphism
proof
   let X be RealNormSpace;
   assume X is non trivial; then
   consider DuX be SubRealNormSpace of DualSp DualSp X,
    L be Lipschitzian LinearOperator of X, DuX such that
A1: L is bijective & DuX = Im(BidualFunc X)
  & (for x be Point of X holds L.x = BiDual x)
  & for x be Point of X holds ||.x.|| = ||. L.x .|| by IMDDX;
   L is isomorphism by A1;
   hence thesis by A1;
end;
