Let's say I have a collision resistant hash function $H: \{0,1\}^* \rightarrow \{0,1\}^n$ and I want to create another collision resistant hash function $H': \{0,1\}^* \rightarrow \{0,1\}^n$ using $H$ that leaks a bit of input. Would this still constitute a collision resistant hash function?
$$H'(x\mathbin\Vert b) = H(x)_{[1\ldots n-1]} \mathbin\| b$$
(Here, $b$ is a single bit)
