| ∀ x0 : (ι → (ι → ι) → ι) → ι → ι → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι → ι → (ι → ι) → ι) → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι → ι → ι) → ι → ι . (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 = Inj1 (Inj1 (x4 (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . Inj1 0) (setsum 0 0)) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . Inj1 0) x5)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 = x4) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι) → ι . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x10) 0 = setsum (Inj1 (x6 (λ x9 . 0) (x7 (λ x9 x10 . Inj0 0)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x2 (λ x13 x14 x15 . λ x16 : ι → ι . x1 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . x15) 0) (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι . x11) 0)) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . setsum 0 0) (x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . x16) 0)) 0 (Inj1 0)) 0 = setsum 0 0) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6) (setsum (x2 (λ x9 x10 x11 . λ x12 : ι → ι . x0 (λ x13 . λ x14 : ι → ι . 0) (setsum 0 0) x11) 0) x6) = x6) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 . λ x10 : ι → ι . 0) (Inj1 (x4 (Inj1 0) 0 (setsum (x6 0) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)) 0)) (x0 (λ x9 . λ x10 : ι → ι . x7) (x4 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7) (setsum 0 0)) (setsum (x6 0) 0) 0 (Inj0 (Inj0 0))) (Inj1 x7)) = setsum 0 0) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 x15 . x1 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . x15) 0) (x0 (λ x11 . λ x12 : ι → ι . setsum 0 0) (setsum 0 (Inj0 0)) (x0 (λ x11 . λ x12 : ι → ι . 0) (setsum 0 0) 0))) 0 (x0 (λ x9 . λ x10 : ι → ι . setsum (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 x15 . 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . 0) 0)) (x7 (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0)) (λ x11 : ι → ι . 0) (setsum 0 0) (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0)))) (x5 (x0 (λ x9 . λ x10 : ι → ι . x10 0) 0 (x4 0 0 0 0)) (λ x9 x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0) 0)) 0) = x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . x13) (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x7 0 (λ x9 : ι → ι . 0) (x4 0 0 0 0) (Inj1 0))))) ⟶ False |
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