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