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