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