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