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;

theorem
  NOT NOT F = F
  proof
    thus NOT NOT F = id(X\dom NOT F) by Th37
    .= id (X\dom id(X\dom F)) by Th37
    .= id (X\(X\dom F)) by RELAT_1:45
    .= id (X/\dom F) by XBOOLE_1:48
    .= id dom F by XBOOLE_1:28
    .= F by Th45;
  end;
