| ∀ x0 : (ι → ι) → ((ι → ι → ι → ι) → ι) → ι . ∀ x1 : (ι → ((ι → ι → ι) → ι) → ι → (ι → ι) → ι) → (((ι → ι → ι) → ι) → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : ((ι → ι → (ι → ι) → ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x9 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . setsum 0 0)) (λ x10 : ι → (ι → ι) → ι . x9 0 (x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . 0)) (λ x11 . 0) 0)) 0 (λ x10 . Inj1 x7) 0) (λ x9 : ι → (ι → ι) → ι . Inj0 0) = Inj1 x7) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0) = x5) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x2 (λ x9 x10 . x10) (x2 (λ x9 x10 . 0) (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . setsum 0 x5) (λ x9 : ι → (ι → ι) → ι . Inj0 x6))) = x2 (λ x9 x10 . setsum x6 0) (setsum x6 0)) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 x10 . x6 (λ x11 : ι → ι → ι . 0)) (x0 (λ x9 . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x6 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → (ι → ι) → ι . x0 (λ x11 . x2 (λ x12 x13 . 0) 0) (λ x11 : ι → ι → ι → ι . x0 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0)))) (λ x9 : ι → ι → ι → ι . 0)) = Inj1 0) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x0 (λ x13 . Inj1 0) (λ x13 : ι → ι → ι → ι . x11)) (λ x9 : (ι → ι → ι) → ι . Inj1 x7) (x2 (λ x9 x10 . 0) (setsum (setsum (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0)) (setsum 0 0)) 0)) (λ x9 . 0) = Inj0 (setsum (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . Inj0 (x5 0)) (λ x9 : ι → (ι → ι) → ι . Inj1 x7)) (x2 (λ x9 x10 . 0) (Inj0 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι . 0)))))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : ι → ι . x9) (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) (Inj1 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . setsum 0 0) (λ x10 : ι → (ι → ι) → ι . x9 (λ x11 x12 . 0)))) (λ x10 . Inj1 0)) (x5 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . Inj1 (Inj0 0)) (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 . x0 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . 0)) (λ x12 : ι → ι → ι → ι . Inj1 0)) (x2 (λ x11 x12 . 0) (setsum 0 0)) (λ x11 . 0)) (setsum (Inj1 0) 0)) (λ x9 . x6 (λ x10 . setsum 0 (Inj0 (x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . 0)))) (Inj0 (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι . x3 (λ x11 : ι → ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι . 0))))) = setsum x4 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x7) (λ x9 : ι → (ι → ι) → ι . 0))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . Inj0 0) (λ x9 : ι → ι → ι → ι . 0) = setsum (setsum x4 (x0 (λ x9 . x9) (λ x9 : ι → ι → ι → ι . x2 (λ x10 x11 . x11) (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 (λ x10 . 0))))) x4) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) (λ x9 : ι → ι → ι → ι . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . x2 (λ x11 x12 . x1 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 . λ x16 : ι → ι . x2 (λ x17 x18 . 0) 0) (λ x13 : (ι → ι → ι) → ι . setsum 0 0) (x9 0 0 0) (λ x13 . setsum 0 0)) (x1 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : ι → ι . x13) (λ x11 : (ι → ι → ι) → ι . 0) 0 (λ x11 . x11))) (λ x10 : ι → (ι → ι) → ι . 0)) = Inj1 (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x2 (λ x10 x11 . x0 (λ x12 . x3 (λ x13 : ι → ι → (ι → ι) → ι → ι . 0) (λ x13 : ι → (ι → ι) → ι . 0)) (λ x12 : ι → ι → ι → ι . Inj0 0)) 0) (λ x9 : ι → (ι → ι) → ι . 0))) ⟶ False |
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