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