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