
theorem Th20:
  for I be non empty set, G be Group,
      i be Element of I, g be Element of G,
      a be Function of I,G
  st a = (I --> 1_G) +* (i,g) & g <> 1_G
  holds support(a) = {i}
  proof
    let I be non empty set, G be Group,
        i be Element of I, g be Element of G,
        a be Function of I,G;
    assume that
    A1: a = (I --> 1_G) +* (i,g) and
    A2: g <> 1_G;
    A3: support(a) c= {i} by A1,Th19;
    dom(I --> 1_G) = I by FUNCOP_1:13; then
    a.i = g by A1,FUNCT_7:31; then
    i in support(a) by A2,Def2; then
    {i} c= support(a) by ZFMISC_1:31;
    hence thesis by A3,XBOOLE_0:def 10;
  end;
