| ∀ x0 : (ι → ι → ι) → ι → (ι → (ι → ι) → ι) → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → (ι → ι) → ι) → ι . ∀ x2 : (ι → ι → ι → ι) → ((ι → ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι) → ((ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x6 (Inj1 x7)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) = Inj1 (setsum (x3 (λ x9 . x9) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 (x10 0 0))) (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0))))) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x9 . x9) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) = Inj1 0) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 . setsum x7 0) (λ x9 : ι → ι → ι . λ x10 . x0 (λ x11 x12 . x12) 0 (λ x11 . λ x12 : ι → ι . Inj0 x11)) = x0 (λ x9 x10 . Inj1 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x10)) (λ x9 . λ x10 : ι → ι . Inj1 (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 x10 x11 . x11) (λ x9 : ι → ι → ι . λ x10 . 0) = x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . x3 (λ x13 . 0) (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x3 (λ x17 . 0) (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 (x6 (λ x10 . x7) (setsum 0 x5) (λ x10 . setsum (x2 (λ x11 x12 x13 . 0) (λ x11 : ι → ι → ι . λ x12 . 0)) (setsum 0 0)))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (Inj1 0) (x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum (x13 0 0) (x2 (λ x16 x17 x18 . 0) (λ x16 : ι → ι → ι . λ x17 . 0))))) = setsum (Inj1 x7) (Inj1 (setsum (x4 (x6 (λ x9 . 0) 0 (λ x9 . 0))) (x3 (λ x9 . x0 (λ x10 x11 . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . setsum 0 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (x7 (Inj0 (x11 0)))) = setsum (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x12 (x14 0)))) (x7 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 x10 . setsum (x0 (λ x11 x12 . 0) (Inj0 (x2 (λ x11 x12 x13 . 0) (λ x11 : ι → ι → ι . λ x12 . 0))) (λ x11 . λ x12 : ι → ι . Inj1 (x2 (λ x13 x14 x15 . 0) (λ x13 : ι → ι → ι . λ x14 . 0)))) 0) x5 (λ x9 . λ x10 : ι → ι . x7) = Inj0 x5) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x9 x10 . x9) (Inj1 (Inj0 (x2 (λ x9 x10 x11 . setsum 0 0) (λ x9 : ι → ι → ι . λ x10 . 0)))) (λ x9 . λ x10 : ι → ι . 0) = setsum x6 (x7 (λ x9 x10 : ι → ι . x0 (λ x11 x12 . x2 (λ x13 x14 x15 . x14) (λ x13 : ι → ι → ι . λ x14 . 0)) x6 (λ x11 . λ x12 : ι → ι . Inj1 (x9 0))) (Inj0 0) 0 (x7 (λ x9 x10 : ι → ι . x0 (λ x11 x12 . x1 (λ x13 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0)) (setsum 0 0) (λ x11 . λ x12 : ι → ι . x9 0)) x6 (x3 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x11 0)) (setsum (x5 (λ x9 x10 x11 . 0) 0) (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0)))))) ⟶ False |
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