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