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
  for X, Y be RealLinearSpace holds RLSStruct (# LinearOperators(X,Y),
    Zero_(LinearOperators(X,Y),RealVectSpace(the carrier of X,Y)), Add_(
LinearOperators(X,Y), RealVectSpace(the carrier of X,Y)), Mult_(LinearOperators
(X,Y), RealVectSpace(the carrier of X,Y)) #) is Subspace of RealVectSpace(the
  carrier of X,Y) by Th14,RSSPACE:11;
