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