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