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