
theorem
  for I be non empty set,
      F be Group-Family of I holds
  support(1_product F,F) is empty
  proof
    let I be non empty set,
        F be Group-Family of I;
    for i be object holds not i in support(1_product F,F)
    proof
      let i be object;
      assume i in support(1_product F,F); then
      ex Z being Group st Z = F.i & (1_product F).i <> 1_Z & i in I by Def1;
      hence contradiction by GROUP_7:6;
    end;
    hence thesis by XBOOLE_0:def 1;
  end;
