theorem
  UAEndMonoid UA, MSAEndMonoid (MSAlg UA) are_isomorphic
proof
  set G = UAEndMonoid UA;
  set H = MSAEndMonoid (MSAlg UA);
  ex h be Homomorphism of G,H st h is bijective
  proof
    deffunc F(object) = 0 .--> $1;
    consider h be Function such that
A1: dom h = UAEnd UA & for x be object st x in UAEnd UA holds h.x = F(x)
    from FUNCT_1:sch 3;
    reconsider h as Homomorphism of G, H by A1,Th14;
    h is bijective by A1,Th15;
    hence thesis;
  end;
  hence thesis;
end;
