definition bla : ℕ → ℕ :=
λ a, foo (succ (succ a)) (bla_2 a)
definition bla_1 : ∀ (x : ℕ), 0 < succ x :=
λ x, zero_lt_succ x
definition bla_2 : ∀ (x : ℕ), 0 < succ (succ x) :=
λ x, lt.step (bla_1 x)
definition test_1 [irreducible] : ∀ (x : ℕ), 0 < succ x :=
λ x, zero_lt_succ x
definition test_2 [reducible] : ∀ (x : ℕ), 0 < succ (succ x) :=
λ x, lt.step (test_1 x)
definition tst_1 : ∀ (x : Type.{l_1}) (x_1 : x) (x_2 : list.{l_1} x),
  x_1 :: x_2 = nil.{l_1} → list.no_confusion_type.{0 l_1} false (x_1 :: x_2) nil.{l_1} :=
λ x x_1 x_2, list.no_confusion.{0 l_1}
definition tst : Π {A : Type.{l_1}}, A → list.{l_1} A → bool :=
λ A a l, voo.{(max 1 l_1)} (a :: l) nil.{l_1} (tst_1.{l_1} A a l)