| ∀ x0 : (((((ι → ι) → ι) → 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) → ι . ∀ x2 : (ι → ι → ι → ι) → (ι → (ι → ι → ι) → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → (ι → (ι → ι) → ι → ι) → ι . (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x3 (λ x9 x10 . x3 (λ x11 x12 . setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . Inj0 0)) (setsum 0 x10)) (Inj1 (x6 (λ x11 : (ι → ι) → ι . setsum 0 0))) (λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 x10)) (Inj0 (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x9 . Inj0 (x3 (λ x10 x11 . 0) 0 (λ x10 . λ x11 : ι → ι . λ x12 . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 (Inj1 (x2 (λ x12 x13 x14 . x0 (λ x15 : (((ι → ι) → ι) → ι) → ι . λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . 0) (λ x15 : (ι → ι) → ι → ι . λ x16 x17 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . 0) (λ x15 . 0))))) = x3 (λ x9 x10 . setsum 0 (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x10) (λ x11 . x9))) (setsum (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . 0) (λ x9 . x7)) (setsum 0 (Inj0 (x6 (λ x9 : (ι → ι) → ι . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 . x11)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x3 (λ x9 x10 . x9) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . x11) (λ x12 . setsum x12 (x2 (λ x13 x14 x15 . x12) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)))) = x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x3 (λ x12 x13 . x3 (λ x14 x15 . x15) x11 (λ x14 . λ x15 : ι → ι . λ x16 . Inj0 x14)) (x2 (λ x12 x13 x14 . 0) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x2 (λ x15 x16 x17 . x17) (λ x15 . λ x16 : ι → ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)))) (λ x12 . λ x13 : ι → ι . λ x14 . Inj0 0)) (λ x9 . x9)) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 x10 x11 . x7 x10 (λ x12 . Inj1 0)) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x11) = x7 x5 (λ x9 . Inj1 (setsum (Inj0 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . λ x12 . 0) (λ x10 . 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 x10 x11 . Inj0 0) (λ x9 . λ x10 : ι → ι → ι . λ x11 . 0) = x4) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x1 (λ x15 . λ x16 : ι → (ι → ι) → ι → ι . λ x17 . x16 (x2 (λ x18 x19 x20 . 0) (λ x18 . λ x19 : ι → ι → ι . λ x20 . 0)) (λ x18 . x17) (x16 0 (λ x18 . 0) 0)) (λ x15 . 0)) (λ x12 . λ x13 : ι → ι → ι . λ x14 . x3 (λ x15 x16 . Inj0 0) 0 (λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . x2 (λ x21 x22 x23 . 0) (λ x21 . λ x22 : ι → ι → ι . λ x23 . 0)) (λ x18 . Inj1 0)))) (λ x9 . x9) = x2 (λ x9 x10 x11 . x7) (λ x9 . λ x10 : ι → ι → ι . λ x11 . x7)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . λ x11 . x2 (λ x12 x13 x14 . x11) (λ x12 . λ x13 : ι → ι → ι . λ x14 . 0)) (λ x9 . x0 (λ x10 : (((ι → ι) → ι) → ι) → ι . λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 x16 x17 . Inj1 0) (λ x15 . λ x16 : ι → ι → ι . λ x17 . setsum (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)) (x3 (λ x18 x19 . 0) 0 (λ x18 . λ x19 : ι → ι . λ x20 . 0)))) (λ x10 . setsum (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . λ x13 . x0 (λ x14 : (((ι → ι) → ι) → ι) → ι . λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 x16 . 0)) (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . λ x14 . 0) (λ x12 . 0))) (x0 (λ x11 : (((ι → ι) → ι) → ι) → ι . λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj1 0) (λ x11 . x9) (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . setsum 0 0))) (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . x10 (λ x13 . setsum (x1 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . λ x16 . 0) (λ x14 . 0)) (x3 (λ x14 x15 . 0) 0 (λ x14 . λ x15 : ι → ι . λ x16 . 0))) (setsum (x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (x3 (λ x13 x14 . 0) 0 (λ x13 . λ x14 : ι → ι . λ x15 . 0))))) = Inj0 x5) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 (Inj1 x13)) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x1 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . λ x15 . 0) (λ x13 . x13)) 0) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj1 (x0 (λ x12 : (((ι → ι) → ι) → ι) → ι . λ x13 x14 . λ x15 : ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . 0) (λ x17 . 0)) (λ x12 . x2 (λ x13 x14 x15 . 0) (λ x13 . λ x14 : ι → ι → ι . λ x15 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 x14 . setsum 0 0))) (setsum (setsum 0 (x9 (λ x12 . 0) 0)) (setsum (x7 (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0)) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι . λ x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 . x3 (λ x17 x18 . x3 (λ x19 x20 . 0) x17 (λ x19 . λ x20 : ι → ι . λ x21 . x19)) (x3 (λ x17 x18 . Inj0 0) (setsum 0 0) (λ x17 . λ x18 : ι → ι . λ x19 . x18 0)) (λ x17 . λ x18 : ι → ι . Inj1)) (λ x14 . λ x15 : ι → ι → ι . λ x16 . x1 (λ x17 . λ x18 : ι → (ι → ι) → ι → ι . λ x19 . Inj0 (x2 (λ x20 x21 x22 . 0) (λ x20 . λ x21 : ι → ι → ι . λ x22 . 0))) (λ x17 . 0))) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 x11 . x9 (λ x12 . x0 (λ x13 : (((ι → ι) → ι) → ι) → ι . λ x14 x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 x19 . Inj0 0) (x1 (λ x18 . λ x19 : ι → (ι → ι) → ι → ι . λ x20 . 0) (λ x18 . 0)) (λ x18 . λ x19 : ι → ι . λ x20 . Inj1 0)) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 x15 . x1 (λ x16 . λ x17 : ι → (ι → ι) → ι → ι . λ x18 . setsum 0 0) (λ x16 . x3 (λ x17 x18 . 0) 0 (λ x17 . λ x18 : ι → ι . λ x19 . 0)))) x7) = Inj1 (x3 (λ x9 x10 . 0) 0 (λ x9 . λ x10 : ι → ι . λ x11 . x11))) ⟶ False |
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