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