| ∀ x0 : ((((ι → ι) → ι) → (ι → 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 → ι) → ι → ι) → (ι → ι) → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι) → ι . (∀ x4 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . setsum (x0 (λ x13 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . x2 (λ x18 . Inj0 0) (x3 (λ x18 x19 . λ x20 : (ι → ι) → ι → ι . λ x21 : ι → ι . 0) (λ x18 . 0))) (x2 (λ x13 . Inj1 0) (x11 (λ x13 . 0) 0)) (λ x13 . x3 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . x14) (λ x14 . 0)) (Inj0 (x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x13 . 0)))) (x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x13 . x11 (λ x14 . setsum 0 0) (Inj1 0)))) (λ x9 . 0) = Inj0 0) ⟶ (∀ x4 : (ι → ι → ι) → (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x13 . Inj0 x10)) (λ x9 . setsum x9 0) = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . x15 (λ x17 . 0) x13) (λ x13 . x3 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) (λ x14 . 0))) (λ x9 . x9)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x9 . 0) 0 = x7) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → (ι → ι) → ι → ι . x2 Inj0 (x7 0 (λ x9 . 0) 0) = Inj1 0) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj0 (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x14 (setsum 0 0)) (λ x11 . 0))) (λ x9 . setsum 0 (x1 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x11 . setsum 0 (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . 0) (λ x12 . 0))) (λ x10 . 0))) = x5 (x5 x7 (setsum x7 (x5 (Inj0 0) (x2 (λ x9 . 0) 0)))) (x0 (λ x9 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x10 (λ x14 x15 . x15) (λ x14 . 0) (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) (λ x14 . x13))) 0 (λ x9 . 0) (x6 (λ x9 . λ x10 : ι → ι . setsum (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x11 . 0)) 0) x7))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x10 . x7) (λ x9 . 0) = x7) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x12) (x4 (setsum 0 x7)) (λ x9 . x7) (setsum 0 (x4 (x4 (x0 (λ x9 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . 0) 0 (λ x9 . 0) 0)))) = x4 (setsum 0 (x4 (x0 (λ x9 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . 0) (setsum 0 0) (λ x9 . x2 (λ x10 . 0) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 . 0)))))) ⟶ (∀ x4 : (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x0 (λ x9 : ((ι → ι) → ι) → (ι → ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . Inj1 (setsum (Inj0 (x2 (λ x14 . 0) 0)) (x2 (λ x14 . 0) (setsum 0 0)))) 0 (λ x9 . x7 (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . setsum (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) (λ x14 . 0)) (x13 0)) (λ x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . λ x12 . Inj1 0) (λ x11 . 0)))) 0 = setsum (setsum 0 (x4 (λ x9 x10 . 0) (λ x9 x10 . setsum (Inj1 0) 0))) 0) ⟶ False |
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