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