| ∀ 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 → ι → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → (ι → ι) → ι . ∀ x3 : (ι → ι → ((ι → ι) → ι) → ι) → ι → (((ι → ι) → ι → ι) → ι → ι) → ι . (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 : (ι → ι → ι → ι) → ι → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (Inj0 (x5 (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . setsum (x13 0) (x3 (λ x16 x17 . λ x18 : (ι → ι) → ι . 0) 0 (λ x16 : (ι → ι) → ι → ι . λ x17 . 0))) (λ x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . Inj0 0) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0)) 0 (x6 (λ x11 : ι → ι → ι . Inj0 0)) (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x10) (x0 (λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x11 x12 . 0) 0 0 0 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum 0 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x11 . x9 (λ x12 . 0) (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . x1 (λ x15 : ι → (ι → ι → ι) → ι . λ x16 x17 x18 . 0) 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . x10)))) = x2 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) (x1 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 x19 x20 . 0) 0) (λ x17 : (ι → ι) → ι → ι . λ x18 . x2 (λ x19 . 0) 0 (λ x19 . 0))) (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . x16) 0)) x9 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)) (x2 (λ x9 . 0) 0 (λ x9 . x6 (λ x10 : ι → ι → ι . Inj0 x9))) (λ x9 . setsum 0 (x5 (λ x10 : ι → ι . Inj1 (x6 (λ x11 : ι → ι → ι . 0)))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x4 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (x2 (λ x11 . 0) 0 (λ x11 . 0))))) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 x12 x13 . setsum (x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . Inj1 0) (λ x14 x15 . x0 (λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 x20 . 0) (λ x16 x17 . 0) 0 0 0 0) x12 x11 (x3 (λ x14 x15 . λ x16 : (ι → ι) → ι . 0) 0 (λ x14 : (ι → ι) → ι → ι . λ x15 . 0)) (setsum 0 0)) (Inj0 (Inj0 0)))) = x4 x7) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 . setsum (x7 (x6 (Inj1 0) (λ x10 . x9) (x2 (λ x10 . 0) 0 (λ x10 . 0))) (x7 0 0)) (setsum (x5 (λ x10 : (ι → ι) → ι . setsum 0 0) 0) (Inj1 (x2 (λ x10 . 0) 0 (λ x10 . 0))))) (Inj1 0) (λ x9 . Inj1 (x5 (λ x10 : (ι → ι) → ι . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x0 (λ x15 : ι → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 x19 . 0) (λ x15 x16 . 0) 0 0 0 0) (setsum 0 0)) 0)) = x4 (setsum (setsum (x2 (λ x9 . x5 (λ x10 : (ι → ι) → ι . 0) 0) (x7 0 0) (λ x9 . 0)) (x5 (λ x9 : (ι → ι) → ι . x6 0 (λ x10 . 0) 0) 0)) (x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum x10 x10) 0 (x5 (λ x9 : (ι → ι) → ι . Inj1 0) (x7 0 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj0 0)) (Inj0 (x5 (λ x9 : (ι → ι) → ι . 0) 0)))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj1 (x2 (λ x13 . x2 (λ x14 . 0) 0 (λ x14 . 0)) x12 (λ x13 . x12))) 0)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . x9) (x7 (λ x9 . 0)) (λ x9 . x5) = x7 (λ x9 . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) x5 (λ x10 : (ι → ι) → ι → ι . λ x11 . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x14 (Inj0 0)) (λ x12 x13 . 0) (x2 (λ x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) (setsum 0 0) (λ x12 . 0)) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (setsum 0 (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0)) (setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (Inj0 (x5 0)) = setsum 0 (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . setsum 0 (Inj1 (Inj0 0))) x11) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum x9 (Inj1 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0))) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . x15) x7) (x2 (λ x12 . x10) (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) (Inj1 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0) x7) (λ x12 . x12))) (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . x12) 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . x1 (λ x20 : ι → (ι → ι → ι) → ι . λ x21 x22 x23 . 0) 0) (x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) x15 (x2 (λ x18 . 0) 0 (λ x18 . 0)) (x14 0 (λ x18 x19 . 0))) (x2 (λ x14 . 0) 0 (λ x14 . x14))) x10 (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (setsum (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0)) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . Inj0 0) (λ x13 x14 . x13) (setsum 0 0) (x0 (λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x13 x14 . 0) 0 0 0 0) x10 x12)))) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 x10 . setsum (setsum (x2 (λ x11 . x7) x10 (λ x11 . Inj1 0)) (x2 (λ x11 . x11) 0 (λ x11 . x11))) (setsum 0 (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . x14) (setsum 0 0)))) 0 (x4 (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . Inj0 0) 0)) x5 x5 (x4 0 (x2 (λ x9 . x7) 0 (λ x9 . x7)) 0 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x12 x13 . 0) 0 0 0 0) (Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . x2 (λ x11 . 0) 0 (λ x11 . 0))))) (setsum (setsum x7 (setsum x7 (x2 (λ x9 . 0) 0 (λ x9 . 0)))) (Inj1 (x1 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 x11 x12 . 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0))))) (setsum 0 0) = Inj0 x5) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 : ι → (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . setsum 0 (x2 (λ x14 . x2 (λ x15 . Inj1 0) x12 (λ x15 . x14)) x13 (λ x14 . 0))) (λ x9 x10 . setsum (x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . Inj0 (x13 (λ x14 . 0))) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . Inj0 0) (Inj1 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (x1 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 x15 x16 . 0) 0) 0)) 0) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 . x12) 0 (λ x12 . x2 (λ x13 . x13) (x2 (λ x13 . 0) 0 (λ x13 . 0)) (λ x13 . x0 (λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 x18 . 0) (λ x14 x15 . 0) 0 0 0 0))) (Inj1 (x5 (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . 0) 0 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 . setsum (x2 (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0)) (x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) 0) (λ x11 . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0))) 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x10) (Inj1 (x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x11) (λ x9 : ι → ι . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . x1 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 x13 x14 . 0) (x2 (λ x11 . 0) 0 (λ x11 . x9 (λ x12 . 0) 0)))) 0 0 = x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . 0) (setsum (x0 (λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x3 (λ x17 x18 . λ x19 : (ι → ι) → ι . 0) 0 (λ x17 : (ι → ι) → ι → ι . λ x18 . 0)) (λ x12 x13 . x13) (x2 (λ x12 . 0) 0 (λ x12 . 0)) x9 x10 (x1 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 x14 x15 . 0) 0)) (x2 (λ x12 . x11 (λ x13 . 0)) 0 (λ x12 . 0))) (λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 . 0) (x1 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 x16 x17 . x0 (λ x18 : ι → (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 x22 . 0) (λ x18 x19 . 0) 0 0 0 0) (x11 (λ x14 . 0))) (λ x14 . Inj0 (x11 (λ x15 . 0))))) (x5 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . x7)) ⟶ False |
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