reserve Q,Q1,Q2 for multLoop;
reserve x,y,z,w,u,v for Element of Q;

theorem Th55:
  for f being Function of Q,Q holds
  f in InnAut Q iff f in Mlt ([#] Q) & f.(1.Q) = 1.Q
proof
  let f be Function of Q,Q;
  thus f in InnAut Q implies f in Mlt ([#] Q) & f.(1.Q) = 1.Q
  proof
    assume f in InnAut Q;
    then ex g being Function of Q,Q st
    f = g & g in Mlt ([#] Q) & g.(1.Q) = 1.Q by Def49;
    hence thesis;
  end;
  thus thesis by Def49;
end;
