theorem Th88:
  A,B are_conjugated iff ex g st B = A * g
proof
  thus A,B are_conjugated implies ex g st B = A * g
  proof
    given g such that
A1: A = B * g;
    A * (-g) = B by A1,Th54;
    hence thesis;
  end;
  given g such that
A2: B = A * g;
  A = B * (-g) by A2,Th54;
  hence thesis;
end;
