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