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