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