Whirlpool makes use of the construction 

Now notice that the key schedule for Whirlpool resembles encryption of the cipher key under a pseudo-key defined by the round constants, so that the core of the hashing process could be formally viewed as two interacting encryption lines. Consider the encryption

We could write the final round key for this block as 

Now show that the two hash constructions are essentially equivalent because of the way that the key schedule is defined.

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H = E(Hi-1, Mi) Hi-1 Mi.