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