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