theorem
  G is commutative Group implies for P being Permutation of dom F1 st F2
  = F1 * P holds 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_1:7;
end;
