reserve X for non empty set;
reserve Y for RealLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);
reserve a,b for Real;
reserve u,v,w for VECTOR of RLSStruct(#Funcs(X,the carrier of Y), (FuncZero(X,
    Y)),FuncAdd(X,Y),FuncExtMult(X,Y)#);

theorem Th29:
  for X, Y be RealNormSpace for f be Lipschitzian LinearOperator of X,Y
  holds modetrans(f,X,Y)=f
proof
  let X, Y be RealNormSpace;
  let f be Lipschitzian LinearOperator of X,Y;
  f in BoundedLinearOperators(X,Y) by Def9;
  hence thesis by Def11;
end;
