| (∀ 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) → (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 → ο . (∀ x4 x5 . ∀ x6 : (ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . In (x7 0) x4 ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 (x6 (λ x10 . Inj0 0) (λ x10 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . 0) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) 0) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . In (setsum 0 (Inj1 x6)) (Inj1 (Inj1 (x5 (Inj1 0) (λ x8 : ι → ι . λ x9 . 0)))) ⟶ x3 (λ x8 : (ι → (ι → ι) → ι) → (ι → ι) → ι → ι . λ x9 . λ x10 : ι → ι → ι . λ x11 x12 . Inj1 0) x4 ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . setsum (setsum (setsum (setsum 0 0) 0) (setsum (setsum 0 0) (Inj0 0))) 0) 0 (λ x8 . 0) (λ x8 . setsum (Inj0 (Inj1 (x5 0 (λ x9 : ι → ι . λ x10 . 0)))) 0)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum (setsum 0 0) (Inj0 0)) (setsum (Inj1 0) (setsum 0 0)))) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x6 0) 0 (λ x8 . 0) (λ x8 . 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x8 : ((ι → ι) → ι) → ι . x8 (λ x9 : ι → ι . x7)) 0 (λ x8 . Inj0 (x6 (λ x9 . setsum x8 (Inj0 0)) (λ x9 : ι → ι . λ x10 . setsum x7 (setsum 0 0)) (λ x9 . 0) 0)) (λ x8 . setsum x8 (Inj0 0)) ⟶ False) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . x2 (λ x8 : ((ι → ι) → ι) → ι . Inj0 (setsum (x8 (λ x9 : ι → ι . Inj1 0)) 0)) 0 (λ x8 . 0) (λ x8 . Inj1 (Inj0 (setsum 0 (setsum 0 0)))) ⟶ x1 (λ x8 x9 . setsum 0 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj1 (setsum (setsum (x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) 0 0) (setsum 0 0)) (setsum 0 (x8 (λ x10 : ι → ι . 0))))) (λ x8 . Inj0 (setsum (x6 (λ x9 : (ι → ι) → ι . x9 (λ x10 . 0)) (λ x9 . 0) 0 0) (x6 (λ x9 : (ι → ι) → ι . setsum 0 0) (λ x9 . x7 0 (λ x10 x11 . 0) (λ x10 . 0) 0) (x5 0 0) 0))) (λ x8 . setsum (Inj0 (setsum 0 0)) (Inj1 0)) (Inj1 (x5 (x7 (Inj0 0) (λ x8 x9 . setsum 0 0) (λ x8 . setsum 0 0) (x5 0 0)) (Inj1 (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x8 x9 . 0) (λ x8 : ((ι → ι) → ι) → ι . λ x9 . Inj0 (x6 0)) (λ x8 . 0) (λ x8 . x7) (x6 0) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . 0) 0 (λ x8 . Inj1 (x5 x8 (λ x9 : ι → ι . 0))) (λ x8 . setsum (Inj0 x8) (x6 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 x7 . In (Inj0 x7) (Inj0 x5) ⟶ x2 (λ x8 : ((ι → ι) → ι) → ι . x5) x7 (λ x8 . Inj0 (setsum (Inj1 (setsum 0 0)) 0)) (λ x8 . 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . x9 (λ x10 x11 . x9 (λ x12 x13 . x10))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj0 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ι . In (Inj1 0) (Inj1 (setsum 0 0)) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj0 (setsum 0 (setsum (Inj0 0) (x9 (λ x10 x11 . 0))))) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . Inj1 0) ⟶ x0 (λ x8 . λ x9 : (ι → ι → ι) → ι . Inj1 0) (λ x8 : ((ι → ι) → ι) → ι → ι → ι . setsum 0 (x5 (λ x9 . 0)))) ⟶ False) ⟶ ∀ x0 : ο . x0 |
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