
theorem Th13:
  for X be non empty set for Y be RealNormSpace for f be bounded
  Function of X,the carrier of Y holds modetrans(f,X,Y)=f
proof
  let X be non empty set;
  let Y be RealNormSpace;
  let f be bounded Function of X,the carrier of Y;
  f in BoundedFunctions(X,Y) by Def5;
  hence thesis by Def7;
end;
