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