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

theorem
  for X be non empty set, Y be ComplexLinearSpace, f,g,h be VECTOR of
ComplexVectSpace(X,Y) holds h = f+g iff for x be Element of X holds h.x = f.x +
  g.x by LOPBAN_1:1;
