 reserve G for Group;
 reserve H for Subgroup of G;
 reserve a, b, c, x, y for Element of G;
 reserve h for Homomorphism of G, G;
 reserve q, q1 for set;

theorem
  for f being Element of InnAut G for g being Element of InnAutGroup G
  st f = g holds f" = g"
proof
  let f be Element of InnAut G;
  let g be Element of InnAutGroup G;
  g is Element of AutGroup G by GROUP_2:42;
  then consider g1 be Element of AutGroup G such that
A1: g1 = g;
  f is Element of Aut G by Th12;
  then consider f1 be Element of Aut G such that
A2: f1 = f;
  assume f = g;
  then f1" = g1" by A2,A1,Th10;
  hence thesis by A2,A1,GROUP_2:48;
end;
