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