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