
theorem Th5:
  for I be non empty set,
      G be Group,
      H be Subgroup of G,
      x be finite-support Function of I,G
  st rng x c= [#]H
  holds x is finite-support Function of I,H
  proof
    let I be non empty set,
        G be Group,
        H be Subgroup of G,
        x be finite-support Function of I,G;
    assume rng x c= [#]H; then
    reconsider y = x as Function of I,H by FUNCT_2:6;
    support x = support y by Th3;
    hence thesis by GROUP_19:def 3;
  end;
