| ∀ x0 : (ι → ι) → (ι → ι) → (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x1 : (((((ι → ι) → ι) → ι → ι → ι) → 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 → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) (λ x10 : ι → ι → ι → ι . 0)) (x5 (λ x9 : (ι → ι) → ι . x7) (λ x9 : ι → ι . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . x9 (Inj0 0)) (λ x10 : ι → ι → ι → ι . x7))) = x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . setsum (setsum (x3 (λ x10 . x7) 0) x7) (x9 (λ x10 : (ι → ι) → ι . λ x11 x12 . x1 (λ x13 : (((ι → ι) → ι) → ι → ι → ι) → ι . x3 (λ x14 . 0) 0) (λ x13 : ι → ι → ι → ι . x13 0 0 0)))) (λ x9 : ι → ι → ι → ι . Inj0 x6)) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 . x9) (setsum (x2 (λ x9 : (ι → ι → ι) → ι . x5) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 : ι → ι . x7) 0) (Inj1 x5)) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x9 : (ι → ι → ι) → ι . x7 (λ x10 : ι → ι . x10 (x9 (λ x11 x12 . x10 0))) (λ x10 : ι → ι . x0 (λ x11 . setsum 0 (x1 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x12 : ι → ι → ι → ι . 0))) (λ x11 . x1 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ι . Inj1 0) (λ x12 : ι → ι → ι → ι . 0)) (λ x11 x12 x13 . 0) (λ x11 : ι → ι . λ x12 . 0)) (λ x10 . x10)) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 : ι → ι . Inj0 (Inj1 (x3 (λ x12 . x12) 0))) 0 = setsum 0 (setsum (x7 (λ x9 : ι → ι . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι . λ x12 x13 . 0)) (λ x10 : ι → ι → ι → ι . x2 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 x13 : ι → ι . 0) 0)) (λ x9 : ι → ι . setsum 0 (x6 (λ x10 : ι → ι . 0))) (λ x9 . Inj0 0)) 0)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 . setsum (x3 (λ x11 . setsum 0 0) (x3 (λ x11 . 0) 0)) x7) 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 : ι → ι . x0 (λ x12 . setsum (x9 (setsum 0 0) (λ x13 . Inj0 0) (x0 (λ x13 . 0) (λ x13 . 0) (λ x13 x14 x15 . 0) (λ x13 : ι → ι . λ x14 . 0))) 0) (λ x12 . 0) (λ x12 x13 x14 . 0) (λ x12 : ι → ι . λ x13 . setsum (x10 (x10 0)) (x0 (λ x14 . 0) (λ x14 . x2 (λ x15 : (ι → ι → ι) → ι . 0) (λ x15 : ι → (ι → ι) → ι → ι . λ x16 x17 : ι → ι . 0) 0) (λ x14 x15 x16 . x1 (λ x17 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x17 : ι → ι → ι → ι . 0)) (λ x14 : ι → ι . λ x15 . Inj0 0)))) (x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . x5 (λ x10 x11 x12 . 0) (λ x10 . setsum (Inj1 0) (Inj0 0))) (λ x9 : ι → ι → ι → ι . x3 (λ x10 . 0) (x9 (x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x10 : ι → ι → ι → ι . 0)) x6 0))) = Inj1 (x3 (λ x9 . Inj1 x7) (Inj1 (x3 (λ x9 . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x10 : ι → ι → ι → ι . 0)) (x5 (λ x9 x10 x11 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . Inj0 x5) (λ x9 : ι → ι → ι → ι . x5) = x5) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . x6) (λ x9 : ι → ι → ι → ι . 0) = setsum x4 (x3 (λ x9 . x7) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ι → ι . x0 (setsum 0) (λ x9 . x6 (λ x10 x11 . x7 (x0 (λ x12 . x2 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 : ι → ι . 0) 0) (λ x12 . x0 (λ x13 . 0) (λ x13 . 0) (λ x13 x14 x15 . 0) (λ x13 : ι → ι . λ x14 . 0)) (λ x12 x13 x14 . Inj1 0) (λ x12 : ι → ι . λ x13 . Inj1 0)))) (λ x9 x10 x11 . 0) (λ x9 : ι → ι . λ x10 . x10) = Inj0 (x3 (λ x9 . 0) (Inj1 (x6 (λ x9 x10 . x1 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . 0) (λ x11 : ι → ι → ι → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x7 . x0 (λ x9 . x9) (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 . x0 (λ x12 . setsum 0 x9) (x10 (λ x12 . x10 (λ x13 . 0) 0)) (λ x12 x13 x14 . 0) (λ x12 : ι → ι . λ x13 . x0 (λ x14 . x13) (λ x14 . 0) (λ x14 x15 x16 . setsum 0 0) (λ x14 : ι → ι . λ x15 . x2 (λ x16 : (ι → ι → ι) → ι . 0) (λ x16 : ι → (ι → ι) → ι → ι . λ x17 x18 : ι → ι . 0) 0))) x9) (λ x9 x10 x11 . x10) (λ x9 : ι → ι . λ x10 . 0) = Inj1 (Inj1 0)) ⟶ False |
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