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