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