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