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;

theorem Th38:
  dom NOT NOT O = dom O
  proof
    thus dom NOT NOT O = dom id(X\dom NOT O) by Th37
    .= X\dom NOT O by RELAT_1:45 .= X\dom id(X\dom O) by Th37
    .= X\(X\dom O) by RELAT_1:45 .= X/\dom O by XBOOLE_1:48
    .= dom O by XBOOLE_1:28;
  end;
