| (∀ x0 : ((ι → ι) → ι → (ι → ι → ι) → ι) → ι → ο . ∀ x1 : (ι → (ι → ι) → ((ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι) → (ι → ι) → (ι → ι → ι) → ο . ∀ x2 : (((ι → (ι → ι) → ι) → ι) → ((ι → ι) → (ι → ι) → ι) → ι → ι) → ι → ο . ∀ x3 : ((((ι → ι → ι) → ι → ι → ι) → ι) → ι) → (((ι → ι) → ι) → ι) → ο . (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 0) (Inj1 (setsum (Inj0 0) (x5 0 (Inj0 0)))) ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . x6) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . setsum x7 (setsum (x6 (setsum 0 0)) 0)) (λ x8 : (ι → ι) → ι . setsum (x8 (λ x9 . 0)) (Inj1 (Inj0 (Inj0 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . setsum 0 x7) (setsum (Inj1 0) (setsum (Inj0 0) (Inj1 (Inj1 0))))) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . In (Inj1 (setsum 0 (setsum 0 0))) (Inj1 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) (x7 (λ x8 : ι → ι → ι . λ x9 : ι → ι . λ x10 . x8 (Inj0 (setsum 0 0)) (x9 (setsum 0 0)))) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . setsum (setsum (setsum (x7 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0)) (setsum 0 0)) (Inj1 (setsum 0 0))) (x9 (λ x11 . setsum (Inj1 0) (x8 (λ x12 . λ x13 : ι → ι . 0))) (λ x11 . 0))) (x4 (λ x8 x9 : ι → ι . λ x10 . x8 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . 0) 0 ⟶ x3 (λ x8 : ((ι → ι → ι) → ι → ι → ι) → ι . 0) (λ x8 : (ι → ι) → ι . 0)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x6 x7 . In (Inj0 (x4 (λ x8 x9 x10 . 0))) (Inj0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 x7) 0 ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj1 (x9 x8)) (λ x8 : ι → ι . Inj1 (setsum (x8 (setsum 0 0)) (Inj0 (Inj0 0)))) (λ x8 . Inj1 (Inj0 0)) (λ x8 x9 . 0)) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj0 (x10 (λ x12 . 0) x8)) (λ x8 : ι → ι . setsum x7 (setsum (setsum 0 (setsum 0 0)) x7)) (λ x8 . 0) (λ x8 x9 . 0) ⟶ In (Inj1 (setsum (x5 (λ x8 x9 : ι → ι . λ x10 . Inj0 0) x4 (λ x8 . setsum 0 0) x7) (Inj0 0))) (setsum (setsum x7 (setsum 0 (setsum 0 0))) (setsum (setsum (setsum 0 0) x4) x6))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . In x7 (setsum 0 0) ⟶ x2 (λ x8 : (ι → (ι → ι) → ι) → ι . λ x9 : (ι → ι) → (ι → ι) → ι . λ x10 . Inj1 (setsum 0 (Inj0 0))) (x6 (setsum (setsum (x6 0) 0) (x6 (Inj1 0)))) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . Inj1 0) (x6 (Inj0 (setsum (setsum 0 0) 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . In (Inj0 (Inj1 0)) x5 ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . x8 x9) (x4 (λ x8 . λ x9 : ι → ι . λ x10 . 0)) ⟶ x0 (λ x8 : ι → ι . λ x9 . λ x10 : ι → ι → ι . 0) 0) ⟶ False) ⟶ ∀ x0 : ο . x0 |
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