theorem
  U1,U2 are_similar implies
    Inv (the carrier of U1,the carrier of U2)
      is Function of the carrier of [:U1,U2:], the carrier of [:U2,U1:]
proof
  assume U1,U2 are_similar;
  then
  [:U1,U2:] = UAStr (# [:the carrier of U1,the carrier of U2:], Opers(U1,
U2) #) & [:U2,U1:] = UAStr (# [:the carrier of U2,the carrier of U1:], Opers(U2
    , U1) #) by Def5;
  hence thesis;
end;
