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