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