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