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