
theorem Th13: :: GROUP_4:18 but about a different Product
  for L being associative commutative unital non empty multMagma
, f, g being FinSequence of L, p being Permutation of dom f st g = f * p holds
  Product(g) = Product(f)
proof
  let L be associative commutative unital non empty multMagma, f, g be
  FinSequence of L, p be Permutation of dom f such that
A1: g = f * p;
  set mL = (the multF of L);
  mL is commutative & mL is associative by MONOID_0:def 11;
  hence thesis by A1,FINSOP_1:7;
end;
