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