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