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