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