User blog comment:Kite in rainbow/A weak and clear version of my Bracket-Comma notation ver2,it reaches Γ(0)/@comment-5529393-20160205064616

In your second example you have 3>>[] [ [] [ [] ] ]=[] [ [] ] [ [] [] ] [ [] [] [] ]. But if X = [] [ [] [ [] ] ], then X(1) = 0 and X(2) = [] [ [] ], so S(X(1)) = {} and 0 >> X(2) = [], and 0 >> X(2) is not contained in S(X(1)) as required by rule (4)((2)).