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