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