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