reserve n for non zero Element of NAT;
reserve a,b,r,t for Real;

theorem Th12:
  for X be non empty closed_interval Subset of REAL, Y be RealNormSpace holds
  0. R_VectorSpace_of_ContinuousFunctions(X,Y) = X -->0.Y
proof
  let X be non empty closed_interval Subset of REAL;
  let Y be RealNormSpace;
  R_VectorSpace_of_ContinuousFunctions(X,Y) is Subspace of
  R_VectorSpace_of_BoundedFunctions(X,Y)
  & 0.R_VectorSpace_of_BoundedFunctions(X,Y) =(X -->0.Y)
    by RSSPACE4:10,RSSPACE:11;
  hence thesis by RLSUB_1:11;
end;
