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 of bool X holds
  ROUGH(A,n,m) c= ROUGH(A,n)
  proof
    let A be FinSequence of bool X;
    let z be object; assume
A1: z in ROUGH(A,n,m); then
    z in {x: n <= #occurrences(x,A) & #occurrences(x,A) <= m} by Def25; then
    ex x st z = x & n <= #occurrences(x,A) & #occurrences(x,A) <= m; then
    z in {x: n <= #occurrences(x,A)};
    hence z in ROUGH(A,n) by A1,Def24;
  end;
