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