Module Type LocalNat.
Inductive nat : Set :=
| O : nat
| S : nat->nat.
Check nat.
Check O.
Check S.
End LocalNat.
Print nat.
Print le.
Print zero_leq_three.
repeat constructor.
Qed.
Print list.
Check list.
Check (nil (A:=nat)).
Check (nil (A:= nat -> nat)).
Check (fun A: Set => (cons (A:=A))).
Check (cons 3 (cons 2 nil)).
Print Vector.t.
Check (Vector.nil nat).
Check (fun (A:Set)(a:A)=> Vector.cons _ a _ (Vector.nil _)).
Check (Vector.cons _ 5 _ (Vector.cons _ 3 _ (Vector.nil _))).
Print eq_3_3.
Print eq_proof_proof.

Lemma eq_lt_le : ( 2 < 4) = (3 <= 4).