reserve X,Y,z,s for set, L,L1,L2,A,B for List of X, x for Element of X,
  O,O1,O2,O3 for Operation of X, a,b,y for Element of X, n,m for Nat;
reserve F,F1,F2 for filtering Operation of X;
reserve i for Element of NAT;

theorem
  for A being FinSequence, a being set st #occurrences(a,A) = len A holds
  max# A = len A
  proof
    let A be FinSequence;
    let a be set;
    assume #occurrences(a,A) = len A; then
    len A <= max# A & max# A <= len A by Def23,Th56;
    hence max# A = len A by XXREAL_0:1;
  end;
