reserve U1,U2,U3 for Universal_Algebra,
  n,m for Nat,
  x,y,z for object,
  A,B for non empty set,
  h1 for FinSequence of [:A,B:];
reserve h1 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U1)*,the carrier of U1,
  h2 for homogeneous quasi_total non empty PartFunc of
    (the carrier of U2)*,the carrier of U2;

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;
