reserve X for non empty set;
reserve Y for ComplexLinearSpace;
reserve f,g,h for Element of Funcs(X,the carrier of Y);

theorem Th1:
  for x being Element of X holds (FuncZero(X,Y)).x = 0.Y
proof
  let x be Element of X;
  thus (FuncZero(X,Y)).x = (X --> 0.Y).x by LOPBAN_1:def 3
    .= 0.Y by FUNCOP_1:7;
end;
