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Bit based division property is a great method of Integral attack on block ciphers, which was invented by Y. Todo. According to the paper Bit-Based Division Property and Application to Simon Family (in proceedings of FSE 2016), how does the set $[11110000]$ will propagate bellow sets?

$[11110000]\rightarrow [11110000]; [11000010]; [01110010];$
$[01100001] \rightarrow [01100001]; [01000011];$
$[10110001]\rightarrow [10110001]; [10000011]; [00110011]$

Furthermore, what means the state "Finally, since the round key is XORed with the right half, the parity of $\pi_{[00001111]}(x)$ for all $x\in X$ becomes unknown"

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