(* 
The typical scheme for programming on natural numbers is

Fixpoint some_program (n: nat) : type_of_result :=
  match n with
  | O => ...
  | S p =>  ... (some_program p) ...
  end.

Note that p is structurally smaller than n when n = S p

This note has been added at the beginning of lecture_02.v,
and the presentation of evenb improved accordingly.

As the new version is clearer, you are encouraged to redo lecture2a.v
if you could not complete it before.

*)