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