| ∀ x0 : (ι → ι → ι → ι) → ι → ι → ι → ι . ∀ x1 : (ι → (ι → ι) → ι) → (ι → ι → ι → ι → ι) → ι . ∀ x2 : (ι → (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . x3 (λ x10 . x7) (x3 (λ x10 . x7) 0 (Inj0 0)) x5) 0 (setsum (Inj0 (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) x5)) (x1 (λ x9 . λ x10 : ι → ι . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x11 . x11)) (λ x9 x10 x11 x12 . x2 (λ x13 . λ x14 : ι → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . x15 (λ x18 . 0)) (λ x13 . x13)))) = setsum (x0 (λ x9 x10 x11 . 0) x6 0 (setsum 0 (Inj0 (Inj1 0)))) x7) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . x10 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . 0) (λ x14 x15 x16 x17 . 0))))) (setsum (setsum 0 0) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . setsum 0 0)) (x3 (λ x9 . x9) x7 (Inj1 0)) (λ x9 . 0))) (x3 (λ x9 . x6 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x3 (λ x12 . Inj0 0) (x11 0) (x2 (λ x12 . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . 0)))) (x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 (x0 (λ x11 x12 x13 . 0) 0 0 0))) (setsum (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 . x9 (λ x11 . 0) 0) (setsum 0 0) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0))) (Inj0 0))) = Inj0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . x11 (λ x15 . x12 0))) (λ x9 . 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj1 (Inj1 0)) (λ x9 . x5) = Inj0 (x3 Inj1 (setsum (setsum (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . 0)) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x13) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0)))) (x3 (λ x9 . x2 (λ x10 . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x12 0) (λ x9 . x9)) (setsum (x0 (λ x9 x10 x11 . 0) 0 0 0) (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 (x11 (λ x14 . Inj0 (x0 (λ x15 x16 x17 . 0) 0 0 0)))) (λ x9 . x7) = Inj1 (setsum 0 (setsum x7 x6))) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . x9) = setsum (Inj0 0) (x1 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . x1 (λ x12 . λ x13 : ι → ι . x2 (λ x14 . λ x15 : ι → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0)) (λ x12 x13 x14 x15 . x13)) (setsum (setsum 0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . 0))) 0) (λ x9 x10 x11 x12 . Inj0 (x0 (λ x13 x14 x15 . x12) (setsum 0 0) 0 (x3 (λ x13 . 0) 0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . setsum 0 0) (λ x9 x10 x11 x12 . x12) = x6 (setsum (x5 (λ x9 . 0) (setsum 0 (Inj1 0)) (λ x9 . x9)) 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . λ x12 : ι → ι . x11) (λ x11 x12 x13 x14 . x3 (λ x15 . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . x18 (λ x21 . 0)) (λ x16 . Inj0 0)) x11 (setsum x11 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . x9) (x6 (x0 (λ x9 x10 x11 . setsum x11 x11) 0 0 (x4 (λ x9 . λ x10 : ι → ι . λ x11 . x11)))) (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . setsum x10 (x0 (λ x13 x14 x15 . x14) x10 x11 0))) (x7 (λ x9 : (ι → ι) → ι → ι . 0)) = setsum (x7 (λ x9 : (ι → ι) → ι → ι . 0)) (setsum (Inj0 0) 0)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 x10 x11 . setsum (x3 (λ x12 . 0) (x3 (λ x12 . Inj1 0) x9 (x3 (λ x12 . 0) 0 0)) (x3 (λ x12 . 0) (setsum 0 0) x9)) 0) (x0 (λ x9 x10 x11 . x11) 0 (x2 (λ x9 . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0)) (x1 (λ x9 . λ x10 : ι → ι . Inj0 (setsum 0 0)) (λ x9 x10 x11 x12 . setsum x10 (setsum 0 0)))) (x1 (λ x9 . λ x10 : ι → ι . x0 (λ x11 x12 x13 . 0) (Inj0 0) (x2 (λ x11 . λ x12 : ι → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . x12 0) (λ x11 . x11)) (Inj0 0)) (λ x9 x10 x11 x12 . x3 (λ x13 . x1 (λ x14 . λ x15 : ι → ι . x2 (λ x16 . λ x17 : ι → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 . 0)) (λ x14 x15 x16 x17 . x3 (λ x18 . 0) 0 0)) x10 x10)) 0 = setsum (setsum x5 0) 0) ⟶ False |
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