| ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : ((ι → ι) → (ι → ι) → ι) → ((((ι → ι) → ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x2 : (((ι → ι) → ι) → ι → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ((ι → ι) → ι) → ι) → (ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . λ x10 : (ι → ι) → ι . x10 (λ x11 . Inj1 (x3 (λ x12 . λ x13 : (ι → ι) → ι . setsum 0 0) (λ x12 . x12)))) (λ x9 . setsum (Inj0 (setsum (x0 (λ x10 . 0) 0) (x2 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0) (λ x10 . 0)))) (setsum 0 x6)) = setsum (setsum (Inj1 (setsum (setsum 0 0) (Inj0 0))) (Inj0 0)) 0) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x9 . λ x10 : (ι → ι) → ι . setsum (x2 (λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 . setsum 0 0))) (Inj0 0)) (λ x9 . setsum (x0 (λ x10 . 0) (x0 (λ x10 . 0) (x2 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0) (λ x10 . 0)))) (x2 (λ x10 : (ι → ι) → ι . λ x11 x12 . x11) (λ x10 . x0 (λ x11 . x10) x9))) = setsum (setsum (setsum (x4 (Inj1 0) (λ x9 x10 . 0)) (x7 (Inj0 0))) (x2 (λ x9 : (ι → ι) → ι . λ x10 x11 . Inj1 (Inj1 0)) (λ x9 . x1 (λ x10 x11 : ι → ι . Inj0 0) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 . x11 0)))) 0) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 . setsum 0 0) (λ x9 . 0) = x4 0 (x7 (Inj1 (x4 (x7 0 (λ x9 x10 . 0) (λ x9 . 0)) (x7 0 (λ x9 x10 . 0) (λ x9 . 0)) (Inj1 0))) (λ x9 x10 . 0) (λ x9 . x5)) (Inj1 (x2 (λ x9 : (ι → ι) → ι . λ x10 x11 . 0) (λ x9 . x2 (λ x10 : (ι → ι) → ι . λ x11 x12 . x9) (λ x10 . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 : (ι → ι) → ι . λ x10 x11 . setsum (x3 (λ x12 . λ x13 : (ι → ι) → ι . x12) (λ x12 . setsum (Inj0 0) (x3 (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 . 0)))) (Inj1 (Inj0 (Inj0 0)))) (λ x9 . setsum (Inj1 (x2 (λ x10 : (ι → ι) → ι . λ x11 x12 . x1 (λ x13 x14 : ι → ι . 0) (λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0)) (λ x10 . x10))) (setsum (x0 (λ x10 . x2 (λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x11 . 0)) (x1 (λ x10 x11 : ι → ι . 0) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0))) (setsum 0 (setsum 0 0)))) = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 . 0)) (setsum 0 (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 . x2 (λ x13 : (ι → ι) → ι . λ x14 x15 . 0) (λ x13 . 0))))) = x5) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 x10 : ι → ι . x9 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) = x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . 0) (setsum (x3 (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 . setsum 0 0) (x10 (λ x11 . 0))) (λ x9 . Inj1 0)) x4) = setsum x4 (Inj1 x4)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x0 (λ x9 . x1 (λ x10 x11 : ι → ι . Inj0 (Inj1 (x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0))) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 . x9)) (x1 (λ x9 x10 : ι → ι . x7 (λ x11 . x10 (Inj1 0)) (λ x11 : ι → ι . λ x12 . x2 (λ x13 : (ι → ι) → ι . λ x14 x15 . setsum 0 0) (λ x13 . x11 0)) (λ x11 . 0) (x0 (λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 . 0)) (Inj0 0))) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . setsum (Inj1 0) (x3 (λ x15 . λ x16 : (ι → ι) → ι . 0) (λ x15 . 0))) (λ x12 . 0))) = x1 (λ x9 x10 : ι → ι . x7 (λ x11 . setsum (x0 (λ x12 . 0) x11) x11) (λ x11 : ι → ι . λ x12 . x12) (λ x11 . x9 (setsum (x2 (λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x12 . 0)) 0)) (x9 (setsum (Inj0 0) (x10 0)))) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 . x1 (λ x13 x14 : ι → ι . x3 (λ x15 . λ x16 : (ι → ι) → ι . setsum 0 0) (λ x15 . Inj1 0)) (λ x13 : ((ι → ι) → ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0)) (x7 (λ x12 . x0 (λ x13 . x10 0) (Inj0 0)) (λ x12 : ι → ι . λ x13 . x0 (λ x14 . Inj0 0) (x2 (λ x14 : (ι → ι) → ι . λ x15 x16 . 0) (λ x14 . 0))) (λ x12 . x11) (Inj0 (x7 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) 0))))) ⟶ False |
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