reserve k,n,i,j for Nat;

theorem
  for n being Nat, K being commutative Ring, p being Element of
  Permutations(n), f,g being FinSequence of K st n>=1 & len f=n & g=f*p holds (
  the multF of K) $$ f = (the multF of K) $$ g by Th30,Th31;
