[Haskell-cafe] bottom case in proof by induction

Dear all, Happy New Year! I am learning the Induction Proof over Haskell, I saw some proofs for the equivalence of two functions will have a case called 'bottom' but some of them do no have. What kind of situation we should also include the bottom case to the proof? How about the functions do not have the 'bottom' input such as: foo [] = [] foo (x:xs) = x : (foo xs) thank you, Raeck