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 L1,L2 being List of X holds
  ROUGH(<*L1,L2*>,2) = L1 AND L2
  proof
    let L1,L2 be List of X;
    len <*L1,L2*> = 2 & rng <*L1,L2*> = {L1,L2} & meet {L1,L2} = L1 AND L2
    by FINSEQ_1:44,FINSEQ_2:127,SETFAM_1:11;
    hence ROUGH(<*L1,L2*>,2) = L1 AND L2 by Th62;
  end;
