| ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → ι → ι → ι → ι) → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x2 : (ι → ι → ι) → ι → ι → ι → ι . ∀ x3 : ((ι → ι → ι) → ι) → (((ι → ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . setsum 0 (x3 (λ x12 : ι → ι → ι . x12 0 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0))) (Inj1 (Inj0 x7)) 0 (x5 (Inj1 (x5 0)))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . Inj1 (x3 (λ x13 : ι → ι → ι . x12) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x14))) = Inj0 (Inj0 (x2 (λ x9 x10 . x2 (λ x11 x12 . x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)) 0 (x6 (λ x11 . 0)) 0) (setsum (x0 (λ x9 . 0) 0) (Inj1 0)) (setsum (setsum 0 0) x7) 0))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι → ι → ι . x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) = setsum 0 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 (setsum (x9 (λ x11 . 0) 0) x6)) (x0 (λ x9 . 0) (x3 (λ x9 : ι → ι → ι . x2 (λ x10 x11 . 0) 0 0 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . 0) 0))) (x4 0 (setsum 0 (setsum 0 0))) (Inj1 (x4 (x5 (λ x9 x10 x11 . 0) (λ x9 . 0) 0 0) (Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ι → ι → ι → ι . x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . x0 (λ x11 . 0) x9) x6 (setsum 0 (x5 (λ x9 x10 x11 . 0))) (setsum x4 (Inj1 (setsum 0 0)))) (x3 (λ x9 : ι → ι → ι . x9 (x9 0 (x5 (λ x10 x11 x12 . 0))) (x2 (λ x10 x11 . setsum 0 0) 0 (Inj0 0) (Inj0 0))) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12)) 0 = setsum (setsum 0 (setsum (x0 (λ x9 . x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) x6) 0)) 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 x10 . x1 Inj0 (λ x11 x12 x13 x14 . setsum x11 x13) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 . 0) 0) (setsum (x2 (λ x11 x12 . 0) (x6 0) (setsum 0 0) x9) (setsum 0 (x2 (λ x11 x12 . 0) 0 0 0))) (λ x11 . setsum x10 (Inj0 (x0 (λ x12 . 0) 0)))) (Inj1 (Inj0 0)) (setsum (setsum (x6 (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) 0) (setsum (setsum (setsum 0 0) (setsum 0 0)) (Inj0 (x2 (λ x9 x10 . 0) 0 0 0)))) (Inj0 (Inj0 (x2 (λ x9 x10 . 0) (x6 0) (setsum 0 0) 0))) = setsum (setsum (x2 (λ x9 x10 . 0) (x6 x4) (setsum (x2 (λ x9 x10 . 0) 0 0 0) (Inj0 0)) (setsum (x3 (λ x9 : ι → ι → ι . 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) x7)) x4) (x6 x4)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 . x7) (λ x9 x10 x11 x12 . x2 (λ x13 x14 . 0) (x3 (λ x13 : ι → ι → ι . 0) (λ x13 : (ι → ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . Inj1 (x1 (λ x17 . 0) (λ x17 x18 x19 x20 . 0) (λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 (λ x17 . 0)))) (Inj1 (x0 (λ x13 . x2 (λ x14 x15 . 0) 0 0 0) (x1 (λ x13 . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 (λ x13 . 0)))) x10) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x9 (Inj0 (x2 (λ x12 x13 . Inj1 0) (x0 (λ x12 . 0) 0) 0 0)) (x0 (λ x12 . setsum (x9 0 0) (x9 0 0)) (x1 (λ x12 . setsum 0 0) (λ x12 x13 x14 x15 . 0) (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 0) 0 (λ x12 . 0)))) 0 (λ x9 . x6) = Inj1 (setsum 0 (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (setsum (Inj1 (x6 (x7 0) (x6 0 0))) 0) (λ x9 . setsum (x3 (λ x10 : ι → ι → ι . x3 (λ x11 : ι → ι → ι . x10 0 0) (λ x11 : (ι → ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 0)) (x3 (λ x10 : ι → ι → ι . 0) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) = x4 (λ x9 . x7 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x6) (x4 0 (setsum 0 (x2 (λ x9 x10 . 0) (x2 (λ x9 x10 . 0) 0 0 0) (x1 (λ x9 . 0) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . 0)) x6))) = x4 (x5 (λ x9 . λ x10 : ι → ι . x0 (λ x11 . Inj1 x9) x9) (Inj1 (x0 (λ x9 . x5 (λ x10 . λ x11 : ι → ι . 0) 0) (x2 (λ x9 x10 . 0) 0 0 0)))) (setsum x7 (x4 0 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 . x3 (λ x10 : ι → ι → ι . setsum (setsum (Inj0 0) (Inj0 0)) (x0 (λ x11 . x0 (λ x12 . 0) 0) (x0 (λ x11 . 0) 0))) (λ x10 : (ι → ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (x0 (λ x14 . x13) 0))) (setsum (setsum (x0 (λ x9 . x1 (λ x10 . 0) (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (λ x10 . 0)) 0) (x3 (λ x9 : ι → ι → ι . x5 0 0 (λ x10 . 0) 0) (λ x9 : (ι → ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0))) (x2 (λ x9 x10 . x0 (λ x11 . x3 (λ x12 : ι → ι → ι . 0) (λ x12 : (ι → ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) 0) 0 (Inj1 (x0 (λ x9 . 0) 0)) (Inj1 0))) = Inj0 0) ⟶ False |
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