| ∀ x0 : (((ι → ι) → ι → (ι → ι) → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι . ∀ x3 : (ι → ι) → ((((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι) → ι . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x3 (λ x9 . Inj1 (x3 (λ x10 . x3 (λ x11 . x7 (λ x12 : (ι → ι) → ι → ι . 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . Inj1 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x2 (λ x12 : ι → ι . x2 (λ x13 : ι → ι . x10 (λ x14 . Inj0 0)) (λ x13 : (ι → ι → ι) → ι . x11)) (λ x12 : (ι → ι → ι) → ι . 0)) = x2 (λ x9 : ι → ι . x3 (λ x10 . Inj0 (x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0))) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x0 (λ x13 : (ι → ι) → ι → (ι → ι) → ι → ι . Inj0 (Inj0 0)) (x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . Inj0 0)))) (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 : (ι → ι) → ι → ι . Inj0 (setsum (Inj0 0) (x2 (λ x11 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x0 (λ x10 : (ι → ι) → ι → (ι → ι) → ι → ι . setsum x9 0) x9) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x1 (λ x12 . 0) (setsum (Inj0 x11) 0)) = setsum (x3 (λ x9 . Inj0 (x3 (λ x10 . x1 (λ x11 . 0) 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x11 (λ x13 . 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι) → ι → (ι → ι) → ι → ι . x10 (λ x12 . Inj0 0)))) (Inj1 (x4 (Inj1 x7)))) ⟶ (∀ x4 : (ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . x5) (λ x9 : (ι → ι → ι) → ι . 0) = setsum (x3 (λ x9 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . x1 (λ x12 . x10 (λ x13 . x11)) (Inj1 x11))) (setsum (x6 0) (x3 (λ x9 . x5) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . 0)))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ι . Inj1 0) (λ x9 : (ι → ι → ι) → ι . Inj0 (setsum (x3 (λ x10 . x3 (λ x11 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . x2 (λ x13 : ι → ι . 0) (λ x13 : (ι → ι → ι) → ι . 0))) (x6 (λ x10 . 0) (λ x10 : ι → ι . x10 0)))) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . x1 (λ x9 . x9) 0 = setsum 0 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) (x6 (λ x9 . Inj1 (x1 (λ x10 . x6 (λ x11 . 0) 0 (λ x11 . 0)) 0)) (setsum x7 (x2 (λ x9 : ι → ι . 0) (λ x9 : (ι → ι → ι) → ι . 0))) (λ x9 . 0)) = Inj1 x7) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x10 . setsum (Inj0 0) 0) 0) (x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . x6 (setsum 0 (x3 (λ x10 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . λ x12 . 0)))) 0) = x1 (λ x9 . x2 (λ x10 : ι → ι . x9) (λ x10 : (ι → ι → ι) → ι . x1 (λ x11 . 0) (setsum (x3 (λ x11 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . λ x13 . 0)) 0))) (setsum (setsum (Inj1 0) x7) x5)) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι → ι . x0 (λ x9 : (ι → ι) → ι → (ι → ι) → ι → ι . Inj1 x6) (Inj0 (Inj0 (x7 0 (setsum 0 0) (x3 (λ x9 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . λ x11 . 0))))) = x5 (x1 (λ x9 . x9) (x4 (λ x9 . setsum 0 0) (λ x9 . Inj0 (x5 0)) (λ x9 . 0) (Inj0 (setsum 0 0))))) ⟶ False |
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