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[<0, 2 >]
     : nat * nat * (nat * nat)
[<0, 2 >]
     : nat * nat * (nat * nat)
(0, 2, (2, 2))
     : nat * nat * (nat * nat)
pair (pair O (S (S O))) (pair (S (S O)) O)
     : prod (prod nat nat) (prod nat nat)
<< 0, 2, 4 >>
     : nat * nat * nat * (nat * (nat * nat))
<< 0, 2, 4 >>
     : nat * nat * nat * (nat * (nat * nat))
(0, 2, 4, (2, (2, 0)))
     : nat * nat * nat * (nat * (nat * nat))
(0, 2, 4, (0, (2, 4)))
     : nat * nat * nat * (nat * (nat * nat))
pair (pair (pair O (S (S O))) (S (S (S (S O)))))
  (pair (S (S (S (S O)))) (pair (S (S O)) O))
     : prod (prod (prod nat nat) nat) (prod nat (prod nat nat))
ETA x y : nat, Nat.add
     : nat -> nat -> nat
ETA x y : nat, Nat.add
     : nat -> nat -> nat
ETA x y : nat, Nat.add
     : nat -> nat -> nat
fun x y : nat => Nat.add x y
     : forall (_ : nat) (_ : nat), nat
ETA x y : nat, le_S
     : forall x y : nat, x <= y -> x <= S y
fun f : forall x : nat * (bool * unit), ?T => CURRY (x : nat) (y : bool), f
     : (forall x : nat * (bool * unit), ?T) ->
       forall (x : nat) (y : bool), ?T@{x:=(x, (y, tt))}
where
?T : [x : nat * (bool * unit) |- Type]