reserve UA for Universal_Algebra,
  f, g for Function of UA, UA;
reserve I for set,
  A, B, C for ManySortedSet of I;
reserve S for non void non empty ManySortedSign,
  U1, U2 for non-empty MSAlgebra over S;

theorem
  UAAutGroup UA, MSAAutGroup (MSAlg UA) are_isomorphic
proof
  deffunc F(object) = 0 .--> $1;
  consider h be Function such that
A1: dom h = UAAut UA & for x be object st x in UAAut UA holds h.x = F(x)
  from FUNCT_1:sch 3;
  reconsider h as Homomorphism of UAAutGroup UA, MSAAutGroup (MSAlg UA)
  by A1,Th33;
  take h;
  thus thesis by A1,Th34;
end;
