
theorem Th4:
  for I be non empty set,
      G be Group,
      H be Subgroup of G,
      y be finite-support Function of I,H
  holds y is finite-support Function of I,G
  proof
    let I be non empty set,
        G be Group,
        H be Subgroup of G,
        y be finite-support Function of I,H;
    [#]H c= [#]G by GROUP_2:def 5; then
    reconsider x = y as Function of I,G by FUNCT_2:7;
    support x = support y by Th3;
    hence thesis by GROUP_19:def 3;
  end;
