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