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(* Testing eta-expansion of elimination predicate *)
Section NATIND2.
Variable P : nat -> Type.
Variable H0 : P 0.
Variable H1 : P 1.
Variable H2 : forall n : nat, P n -> P (S (S n)).
Fixpoint nat_ind2 (n : nat) : P n :=
match n as x return (P x) with
| O => H0
| S O => H1
| S (S n) => H2 n (nat_ind2 n)
end.
End NATIND2.
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