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