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