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