
theorem Th15:
  for I be set,
      G be Group,
      x be finite-support Function of I,G
  st support(x) = {}
  holds Product x = 1_G
  proof
    let I be set,
        G be Group,
        x be finite-support Function of I,G;
    assume support(x) = {}; then
    (x|support(x)) * canFS(support(x)) = <*>(the carrier of G); then
    Product(x|support(x)) = Product(<*>(the carrier of G)) by GROUP_17:def 1
                         .= 1_G by GROUP_4:8;
    hence thesis;
  end;
