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