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