reserve i, I for set,
  f, g, h for Function,
  s for ManySortedSet of I;
reserve G1, G2, G3 for non empty multMagma,
  x1, x2 for Element of G1,
  y1, y2 for Element of G2,
  z1, z2 for Element of G3;
reserve G1, G2, G3 for Group-like non empty multMagma;
reserve G1, G2, G3 for Group,
  x for Element of G1,
  y for Element of G2,
  z for Element of G3;

theorem
  G1, product <*G1*> are_isomorphic
proof
  deffunc F(Element of G1) = <*$1*>;
  consider f being Function of the carrier of G1,
    the carrier of product <*G1*> such that
A1: for x being Element of G1 holds f.x = F(x) from FUNCT_2:sch 4;
  reconsider f as Homomorphism of G1, product <*G1*> by A1,Th37;
  take f;
  thus thesis by A1,Th38;
end;
