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["John Wiegley" <johnw AT newartisans.com>]

>>>>> Cedric Auger 
>>>>> <sedrikov AT gmail.com>
>>>>>  writes:

> You can then define a injection f which sends any (x:fin (S n)) such that
> (x≠hd) to some (y:fin n).

Thanks to you and Daniel, I am now much closer.  However, I'm still having
difficulty with the above statement: what about the case where hd is not the
greatest element of fin (S n)?  Then the fact that x <> hd doesn't help me,
since hd could be an element which *should* be in y, rather than x.  It seems
like your proof assumes an ordered set from greatest to last, when the
original statement requires no ordering.  Daniel did make reference to the
fact that having a sorting property could make things easier.

John