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