On vectors
     Do the same exercise as  this one  , but considering vectors instead of
lists 
    
Solution
Look at  this file 
 See also 
Consider the following definition, very similar to Standard Library's 
definition:
(** Similar to Vector_Def library, with different names 
*)
Section Vector_definitions.
Variable A : Type.
Inductive vector : nat -> Type :=
| vnil : vector 0
| vcons (h:A)(n:nat)(v: vector n) : vector (S n).
Define the functions that return respectively the head and the tail of 
a non-empty vector,  as direct 
applications of the recursor vector_rect>
    
Solution
Look at  this file