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