
theorem
  for p be Prime holds Z/Z*(p) = MultGroup (INT.Ring(p))
proof
  let p be Prime;
A1: 0 in Segm(p) by NAT_1:44;
  then
A2: Segm(p) \ {0} = NonZero INT.Ring p by SUBSET_1:def 8
    .= the carrier of MultGroup (INT.Ring(p)) by UNIROOTS:def 1;
A3: 1 < p by INT_2:def 4;
  then
A4: the multF of Z/Z*(p) = (multint p) || (Segm(p) \ {0}) by INT_7:def 2
    .= the multF of MultGroup (INT.Ring(p)) by A2,UNIROOTS:def 1;
  0 = In (0,Segm(p)) by A1,SUBSET_1:def 8;
  then the carrier of (Z/Z*(p)) = NonZero INT.Ring p by A3,INT_7:def 2
    .= the carrier of MultGroup (INT.Ring(p)) by UNIROOTS:def 1;
  hence Z/Z*(p) = MultGroup (INT.Ring(p)) by A4;
end;
