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