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