
theorem
  for I be non empty set, G be Group,
      a be finite-support Function of I,G,
      i be Element of I, g be Element of G
  holds a +* (i,g) is finite-support Function of I,G
  proof
    let I be non empty set, G be Group,
        a be finite-support Function of I,G,
        i be Element of I, g be Element of G;
    reconsider b = a +* (i,g) as Function of I,G;
    support(a) is finite; then
    support(b) is finite by Th23;
    hence thesis by Def3;
  end;
