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