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