reserve V for non empty RealLinearSpace;
reserve S for Real_Sequence;
reserve k,n,m,m1 for Nat;
reserve g,h,r,x for Real;

theorem Th21:
  for X be RealNormSpace, f be Functional of X st
    (for x be VECTOR of X holds f.x=0) holds f is Lipschitzian
proof
  let X be RealNormSpace;
  let f be Functional of X;
  assume
A1: for x be VECTOR of X holds f.x=0;
  take 0;
  thus thesis by A1,COMPLEX1:44;
end;
