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