[Haskell-beginners] Re: [Haskell-cafe] bottom case in proof by induction

Luke Palmer wrote:

First, by simple definition, id _|_ = _|_. Now let's consider foo _|_. The Haskell semantics say that pattern matching on _|_ yields _|_, so foo _|_ = _|_. So they are equivalent on _|_ also. Thus foo and id are exactly the same function.

Would it in general also be interesting to look at foo == id for input (_|_:xs) and all other possible positions and combinations of positions for bottom? I wonder how many cases you need to take into consideration to have covered every possible situation. Martijn.