Prove Transitivity in Haskell semantics

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I am learning semantics of Haskell and there I came across this question:

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I have tried it but still unable to conclude the answer. It will be great if someone explains me how to prove this one. Thank you.

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  1. Just a sketch -> Since pn(s) for fixed n is morphism Ninf -> N , that is set of Integers into Integer, this proof can be simplified using this relation into proof of transitivity over integers

  2. [1,0,0 .. ] -> [2,0,0 ..] -> [3,0,0 ..] -> ...
    I am sure you can find even more interesting one