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Module Type ELEM.
Parameter A:Set.
Parameter x:A.
End ELEM.
Module Nat.
Definition A:=nat.
Definition x:=O.
End Nat.
Module List[X:ELEM].
Inductive list : Set := nil : list
| cons : X.A -> list -> list.
Definition head :=
[l:list]Cases l of
nil => X.x
| (cons x _) => x
end.
Definition singl := [x:X.A] (cons x nil).
Lemma head_singl : (x:X.A)(head (singl x))=x.
Auto.
Qed.
End List.
Module N:=(List Nat).
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