reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;
reserve E for set,
  A for Action of O,E,
  C for Subset of G,
  N1 for normal StableSubgroup of H1;

theorem
  for O being non empty set, E being set, F1,F2 being FinSequence of O,
A being Action of O,E holds Product(F1^F2,A) = Product(F1,A) * Product(F2,A)
by Lm28;
