theorem
  G is commutative Group & F1 is one-to-one & F2 is one-to-one & rng F1
  = rng F2 implies Product(F1) = Product(F2)
proof
  set g = the multF of G;
  assume G is commutative Group;
  then g is commutative by GROUP_3:2;
  hence thesis by FINSOP_1:8;
end;
