
theorem Th12:
  for I be non empty set, G be Group,
      a be Function of I,G
  st a = I --> 1_G
  holds support(a) is empty
  proof
    let I be non empty set, G be Group,
        a be Function of I,G;
    assume
    A1: a = I --> 1_G;
    for i be object holds not i in support(a)
    proof
      let i be object;
      assume
      A2: i in support(a); then
      a.i = 1_G by A1,FUNCOP_1:7;
      hence contradiction by A2,Def2;
    end;
    hence thesis by XBOOLE_0:def 1;
  end;
