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