reserve p,q,r for FinSequence;
reserve u,v,x,y,y1,y2,z for object, A,D,X,Y for set;
reserve i,j,k,l,m,n for Nat;

theorem
  n in dom p implies
    for B being finite set st
   B = {k where k is Element of NAT : k in dom p & k <= n & p.k in A}
  holds p.n in A or (p - A).(n - card B) = p.n
proof
  len p = len p;
  hence thesis by Lm13;
end;
