reserve i,j for Nat;

theorem Th16:
  for K being non empty multMagma, p being FinSequence of K, a
  being Element of K holds len (a*p)=len p
proof
  let K be non empty multMagma, p be FinSequence of K, a be Element of K;
  reconsider q=p as Element of (len p)-tuples_on the carrier of K by
FINSEQ_2:92;
  a*q in (len p)-tuples_on the carrier of K;
  then
  a*q in { s where s is Element of (the carrier of K)*: len s = len p } by
FINSEQ_2:def 4;
  then ex s being Element of (the carrier of K)* st a*q=s & len s = len p;
  hence thesis;
end;
