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