| ∀ x0 : (ι → ι → ι → ι) → ι → ι . ∀ x1 : (ι → ι → (ι → ι) → ι → ι) → ((ι → ι → ι → ι) → ι → ι → ι) → ι → ι . ∀ x2 : ((ι → ι) → (ι → ι) → (ι → ι) → ι → ι) → (((ι → ι → ι) → ι) → ι) → ι → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → ι) → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x10 (λ x12 : ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . 0) (Inj0 (setsum (x0 (λ x9 x10 x11 . 0) (x4 0)) 0)) = setsum (x7 (λ x9 : ι → ι . Inj1 (x0 (λ x10 x11 x12 . x11) (setsum 0 0))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . Inj0 (setsum 0 0)) (λ x11 : (ι → ι) → ι → ι . 0) (x0 (λ x11 x12 x13 . x11) 0)) (λ x9 . x7 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . Inj0 (Inj0 0)) (λ x10 . x0 (λ x11 x12 x13 . setsum 0 0) 0) 0) (x7 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . x13 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0) 0) (λ x9 . 0) (setsum (x7 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) (setsum 0 0)))) 0) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 . setsum (x2 (λ x12 x13 x14 : ι → ι . λ x15 . x13 0) (λ x12 : (ι → ι → ι) → ι . x10 (λ x13 : ι → ι . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0)) 0 x7) (setsum x9 (Inj1 0))) (λ x9 : (ι → ι) → ι → ι . setsum (Inj0 0) 0) 0 = Inj1 (x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 x15 . x2 (λ x16 x17 x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι → ι) → ι . x15) x12 0) (Inj1 0)) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x0 (λ x12 x13 x14 . setsum (x1 (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : ι → ι → ι → ι . λ x16 x17 . 0) 0) x12) (x1 (λ x12 x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x12 : ι → ι → ι → ι . λ x13 x14 . Inj1 0) x10)) (Inj0 (setsum (x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 0) (setsum 0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . x7 (setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0) 0) (x6 (x7 0) (λ x10 . x6 0 (λ x11 . 0))))) (x7 (Inj1 (Inj0 (setsum 0 0)))) (setsum 0 (x5 (λ x9 x10 : ι → ι . Inj1 (x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . 0) 0)) (λ x9 : ι → ι . x9 (x6 0 (λ x10 . 0))))) = x7 (setsum (x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) (x11 0)) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 x11 : ι → ι . 0) (λ x10 : ι → ι . setsum 0 0)) (x6 0 (λ x9 . 0)) 0) (setsum 0 (x5 (λ x9 x10 : ι → ι . Inj0 0) (λ x9 : ι → ι . Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (Inj1 (Inj0 0)) (setsum 0 (setsum (x9 0) (setsum 0 0)))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 0) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . x0 (λ x14 x15 x16 . x14) 0) (λ x10 : (ι → ι → ι) → ι . x9 (λ x11 x12 . x10 (λ x13 x14 . 0))) x6 0)) (Inj0 0) (setsum x7 x7) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 . 0) (λ x13 : (ι → ι) → ι → ι . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 . x3 (λ x18 . λ x19 : ((ι → ι) → ι) → ι . λ x20 . 0) (λ x18 : (ι → ι) → ι → ι . 0) 0) (λ x15 : (ι → ι) → ι → ι . x1 (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : ι → ι → ι → ι . λ x17 x18 . 0) 0) (x14 (λ x15 x16 . 0))) (setsum (x0 (λ x14 x15 x16 . 0) 0) (x13 (λ x14 . 0) 0)) (setsum (setsum 0 0) (x0 (λ x14 x15 x16 . 0) 0))) (Inj0 (setsum (x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) 0))) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x10) (x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (Inj0 (setsum 0 0)) 0) (λ x9 : (ι → ι → ι) → ι . x5) (Inj1 0) 0) = x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (x9 (x11 x12)) 0) (λ x9 : (ι → ι → ι) → ι . setsum (setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι) → ι → ι . x9 (λ x11 x12 . 0)) 0) (x7 (λ x10 . setsum 0 0))) (setsum 0 0)) (setsum 0 (x7 (λ x9 . x6))) x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι . setsum (x1 (λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj0 x12) (λ x12 : ι → ι → ι → ι . λ x13 x14 . 0) (Inj1 (Inj1 0)))) (λ x9 : ι → ι → ι → ι . λ x10 x11 . Inj1 (x7 (λ x12 . 0))) 0 = x5 (λ x9 x10 . x2 (λ x11 x12 x13 : ι → ι . λ x14 . x12 (x2 (λ x15 x16 x17 : ι → ι . λ x18 . x1 (λ x19 x20 . λ x21 : ι → ι . λ x22 . 0) (λ x19 : ι → ι → ι → ι . λ x20 x21 . 0) 0) (λ x15 : (ι → ι → ι) → ι . Inj1 0) 0 (setsum 0 0))) (λ x11 : (ι → ι → ι) → ι . 0) (Inj1 0) 0) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 . x16) (λ x14 : (ι → ι) → ι → ι . x12 (λ x15 : ι → ι . x3 (λ x16 . λ x17 : ((ι → ι) → ι) → ι . λ x18 . 0) (λ x16 : (ι → ι) → ι → ι . 0) 0)) 0) (λ x11 : (ι → ι) → ι → ι . 0) (Inj1 (setsum (x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . 0) 0) x10)))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 x11 . 0) 0 = Inj0 (setsum (x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x10) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x7) 0) 0)) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 x11 . x2 (λ x12 x13 x14 : ι → ι . λ x15 . 0) (λ x12 : (ι → ι → ι) → ι . Inj1 (x0 (λ x13 x14 x15 . 0) 0)) 0 0) 0 = x2 (λ x9 x10 x11 : ι → ι . λ x12 . x0 (λ x13 x14 x15 . x15) (x11 (setsum (x11 0) (x10 0)))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 (Inj1 (x9 (λ x10 x11 . 0)))) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 . Inj0 0) (λ x14 : (ι → ι) → ι → ι . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 . 0) (λ x15 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0)) (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 x12 x13 . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0) (Inj1 0)) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . Inj1 0) (λ x10 : (ι → ι → ι) → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . 0) (λ x11 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0)) (setsum (Inj1 0) (x0 (λ x10 x11 x12 . 0) 0)))) x4 (x2 (λ x9 x10 x11 : ι → ι . λ x12 . x1 (λ x13 x14 . λ x15 : ι → ι . λ x16 . x14) (λ x13 : ι → ι → ι → ι . λ x14 x15 . x12) x12) (λ x9 : (ι → ι → ι) → ι . Inj1 (setsum (setsum 0 0) 0)) 0 (x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . Inj0 0) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0) 0) x4 0))) ⟶ False |
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