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Proofgold Address

address
PUfTwjJqn9KgYTDe13wpFQScNaicgfN7nHP
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0
mg
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conjpub
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current assets
0aabf../3d773.. bday: 11848 doc published by PrGVS..
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Known notEnotE : ∀ x0 : ο . not x0 ⟶ x0 ⟶ False
Known e3ec9..neq_0_1 : not (0 = 1)
Theorem 45506.. : ∀ x0 : ((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) → (((ι → ι) → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → ι → ι → ((ι → ι) → ι) → ι . ∀ x3 : (ι → ι → ι) → (ι → ι → (ι → ι) → ι) → ι . (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 x10 . x2 (λ x11 . 0) (x1 (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → ι . λ x13 . x1 (λ x14 : (ι → ι → ι) → ι . 0) (λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0)) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x13) (λ x12 : ι → ι . x10) 0 (λ x12 . x10) (Inj0 0)) (λ x11 . λ x12 : ι → ι . λ x13 x14 . Inj0 (x12 0)) (λ x11 : (ι → ι) → ι → ι . 0)) (Inj1 0) (λ x11 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . 0) = x2 (λ x9 . setsum (x1 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) (Inj0 0))) (x3 (λ x10 x11 . x2 (λ x12 . setsum 0 0) 0 (x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) 0 (λ x12 . 0) 0) (λ x12 : ι → ι . x2 (λ x13 . 0) 0 0 (λ x13 : ι → ι . 0))) (λ x10 x11 . λ x12 : ι → ι . 0))) (x5 (x5 (x4 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum 0 0)))) (x4 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0)) (λ x9 : ι → ι . setsum x7 (x9 (x5 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . Inj1 (x0 (λ x12 : ι → ι . λ x13 . setsum x13 x10) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) (Inj1 (x3 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . 0))) (x0 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . λ x15 . 0) (λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x14 : ι → ι . 0) 0 (λ x14 . 0) 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x13) (λ x12 : ι → ι . 0) (x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)) (λ x12 . 0)) 0)) = x4 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum (setsum (x9 (λ x12 . x0 (λ x13 : ι → ι . λ x14 . 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x13 : ι → ι . 0) 0 (λ x13 . 0) 0)) 0) (setsum 0 x11))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 . x5) (Inj0 0) (Inj0 0) (λ x9 : ι → ι . 0) = x5) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 . 0) (x0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . x6 (x7 (Inj0 0)) 0 (λ x10 . x2 (λ x11 . Inj0 0) (x2 (λ x11 . 0) 0 0 (λ x11 : ι → ι . 0)) x10 (λ x11 : ι → ι . x10))) (λ x9 : ι → ι . 0) 0 (λ x9 . 0) (setsum 0 (x3 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . setsum 0 0)))) (x0 (λ x9 : ι → ι . λ x10 . x9 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . 0) (λ x9 : ι → ι . Inj1 0) (x3 (λ x9 . setsum (Inj0 0)) (λ x9 x10 . λ x11 : ι → ι . Inj0 (Inj1 0))) (λ x9 . Inj0 (x2 (λ x10 . x9) 0 (x2 (λ x10 . 0) 0 0 (λ x10 : ι → ι . 0)) (λ x10 : ι → ι . x2 (λ x11 . 0) 0 0 (λ x11 : ι → ι . 0)))) 0) (λ x9 : ι → ι . 0) = x0 (λ x9 : ι → ι . λ x10 . setsum (x9 (x7 (x7 0))) (x0 (λ x11 : ι → ι . λ x12 . x3 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . setsum 0 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . x9 (setsum 0 0)) (λ x11 : ι → ι . 0) (x7 x10) (λ x11 . x1 (λ x12 : (ι → ι → ι) → ι . x12 (λ x13 x14 . 0)) (λ x12 . λ x13 : ι → ι . λ x14 x15 . setsum 0 0) (λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . 0) 0)) (Inj0 0))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . x7 (x6 (x3 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . 0)) (x1 (λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) 0 (λ x12 . 0) 0) (λ x11 . λ x12 : ι → ι . λ x13 x14 . Inj1 0) (λ x11 : (ι → ι) → ι → ι . 0)) (λ x11 . 0) (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . setsum 0 0) (λ x11 : ι → ι . x10) (setsum 0 0) (λ x11 . setsum 0 0) (Inj0 0)))) (λ x9 : ι → ι . x9 (x0 (λ x10 : ι → ι . λ x11 . Inj1 (x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) 0 (λ x12 . 0) 0)) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . x2 (λ x14 . 0) 0 0 (λ x14 : ι → ι . 0)) (λ x12 : ι → ι . Inj1 0) 0 (λ x12 . setsum 0 0) (x7 0)) (λ x10 : ι → ι . x9 (x3 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . 0))) 0 (λ x10 . 0) (x0 (λ x10 : ι → ι . λ x11 . x10 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . Inj0 0) (Inj0 0) (λ x10 . 0) (x6 0 0 (λ x10 . 0) 0)))) (x6 0 (setsum (setsum 0 (x3 (λ x9 x10 . 0) (λ x9 x10 . λ x11 : ι → ι . 0))) (x3 (λ x9 x10 . setsum 0 0) (λ x9 x10 . λ x11 : ι → ι . x10))) (λ x9 . x0 (λ x10 : ι → ι . λ x11 . x9) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . Inj0 0) (λ x10 : ι → ι . x1 (λ x11 : (ι → ι → ι) → ι . Inj0 0) (λ x11 . λ x12 : ι → ι . λ x13 x14 . x2 (λ x15 . 0) 0 0 (λ x15 : ι → ι . 0)) (λ x11 : (ι → ι) → ι → ι . 0)) (Inj1 (x1 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x10 : (ι → ι) → ι → ι . 0))) (λ x10 . 0) (Inj0 0)) (Inj0 (setsum (x7 0) 0))) (λ x9 . x3 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . setsum (x1 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . λ x15 x16 . x0 (λ x17 : ι → ι . λ x18 . 0) (λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x18 . 0) (λ x17 : ι → ι . 0) 0 (λ x17 . 0) 0) (λ x13 : (ι → ι) → ι → ι . setsum 0 0)) 0)) (Inj0 (Inj1 (x6 (x0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . 0) (λ x9 : ι → ι . 0) 0 (λ x9 . 0) 0) 0 (λ x9 . x3 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) 0)))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : (ι → ι → ι) → ι . setsum (x3 (λ x10 x11 . setsum 0 (x3 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . 0))) (λ x10 x11 . λ x12 : ι → ι . 0)) (x7 (x3 (λ x10 x11 . x7 0) (λ x10 x11 . λ x12 : ι → ι . x3 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . 0))))) (λ x9 . λ x10 : ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . x7 (x3 (λ x10 x11 . Inj1 (setsum 0 0)) (λ x10 x11 . λ x12 : ι → ι . 0))) = x7 (Inj1 x4)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x1 (λ x9 : (ι → ι → ι) → ι . x0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 . x11 (Inj0 0)) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . x3 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . 0)) (λ x11 : ι → ι . Inj1 (x9 (λ x12 x13 . 0))) (setsum 0 0) (λ x11 . 0) (x9 (λ x11 x12 . 0))) (x9 (λ x10 x11 . x10)) (λ x10 . x7 (x1 (λ x11 : (ι → ι → ι) → ι . Inj1 0) (λ x11 . λ x12 : ι → ι . λ x13 x14 . x12 0) (λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0))) (λ x11 . 0)) x5) (λ x9 . λ x10 : ι → ι . λ x11 x12 . x11) (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : (ι → ι → ι) → ι . x10 (λ x11 x12 . setsum x12 (x3 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . 0)))) (λ x10 . λ x11 : ι → ι . λ x12 x13 . x2 (λ x14 . setsum x13 0) (x3 (λ x14 x15 . setsum 0 0) (λ x14 x15 . λ x16 : ι → ι . Inj0 0)) 0 (λ x14 : ι → ι . 0)) (λ x10 : (ι → ι) → ι → ι . x7 (x10 (λ x11 . 0) (x2 (λ x11 . 0) 0 0 (λ x11 : ι → ι . 0))) (λ x11 . setsum (x10 (λ x12 . 0) 0) (x7 0 (λ x12 . 0))))) = x1 (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . x2 (λ x13 . x12 x10) (x3 (λ x13 x14 . setsum 0 0) (λ x13 x14 . λ x15 : ι → ι . Inj1 0)) (Inj1 (x9 (λ x13 x14 . 0))) (λ x13 : ι → ι . 0))) (λ x9 . λ x10 : ι → ι . λ x11 x12 . x1 (λ x13 : (ι → ι → ι) → ι . x10 (Inj0 0)) (λ x13 . λ x14 : ι → ι . λ x15 x16 . x13) (λ x13 : (ι → ι) → ι → ι . x2 (λ x14 . setsum (Inj0 0) (x13 (λ x15 . 0) 0)) 0 (x10 (x0 (λ x14 : ι → ι . λ x15 . 0) (λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x14 : ι → ι . 0) 0 (λ x14 . 0) 0)) (λ x14 : ι → ι . x12))) (λ x9 : (ι → ι) → ι → ι . x3 (λ x10 x11 . 0) (λ x10 x11 . λ x12 : ι → ι . 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 : (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x9 : ι → ι . λ x10 . setsum (Inj1 (Inj1 0)) (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . x3 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . x3 (λ x15 x16 . 0) (λ x15 x16 . λ x17 : ι → ι . 0))) 0 (λ x11 . x11) (setsum 0 (Inj0 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . setsum (x7 (λ x11 x12 : ι → ι . Inj1 (Inj1 0)) (x6 (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0)) (setsum (setsum 0 0) 0) (x2 (λ x11 . x11) (x9 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)) (setsum 0 0) (λ x11 : ι → ι . 0))) (x1 (λ x11 : (ι → ι → ι) → ι . x7 (λ x12 x13 : ι → ι . x10) (x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)) (setsum 0 0) x10) (λ x11 . λ x12 : ι → ι . λ x13 x14 . x11) (λ x11 : (ι → ι) → ι → ι . Inj0 0))) (λ x9 : ι → ι . x9 (x7 (λ x10 x11 : ι → ι . setsum (x10 0) 0) (x9 0) (x3 (λ x10 x11 . x9 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (x9 0))) (x4 (λ x9 : (ι → ι) → ι . x9 (λ x10 . x7 (λ x11 x12 : ι → ι . x3 (λ x13 x14 . 0) (λ x13 x14 . λ x15 : ι → ι . 0)) (setsum 0 0) 0 (x9 (λ x11 . 0)))) (λ x9 : ι → ι . setsum 0 (setsum 0 0))) (λ x9 . 0) (x1 (λ x9 : (ι → ι → ι) → ι . x1 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 x13 . Inj0 (Inj0 0)) (λ x10 : (ι → ι) → ι → ι . Inj1 0)) (λ x9 . λ x10 : ι → ι . λ x11 x12 . x1 (λ x13 : (ι → ι → ι) → ι . x3 (λ x14 x15 . x1 (λ x16 : (ι → ι → ι) → ι . 0) (λ x16 . λ x17 : ι → ι . λ x18 x19 . 0) (λ x16 : (ι → ι) → ι → ι . 0)) (λ x14 x15 . λ x16 : ι → ι . x0 (λ x17 : ι → ι . λ x18 . 0) (λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x18 . 0) (λ x17 : ι → ι . 0) 0 (λ x17 . 0) 0)) (λ x13 . λ x14 : ι → ι . λ x15 x16 . x2 (λ x17 . 0) x15 0 (λ x17 : ι → ι . setsum 0 0)) (λ x13 : (ι → ι) → ι → ι . x10 (setsum 0 0))) (λ x9 : (ι → ι) → ι → ι . x7 (λ x10 x11 : ι → ι . x7 (λ x12 x13 : ι → ι . x1 (λ x14 : (ι → ι → ι) → ι . 0) (λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0)) (x2 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0)) (x2 (λ x12 . 0) 0 0 (λ x12 : ι → ι . 0)) 0) 0 (setsum (x2 (λ x10 . 0) 0 0 (λ x10 : ι → ι . 0)) (setsum 0 0)) (setsum (Inj1 0) (x7 (λ x10 x11 : ι → ι . 0) 0 0 0)))) = x4 (λ x9 : (ι → ι) → ι . setsum (setsum (x0 (λ x10 : ι → ι . λ x11 . x0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . 0) 0 (λ x12 . 0) 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x3 (λ x12 x13 . 0) (λ x12 x13 . λ x14 : ι → ι . 0)) (λ x10 : ι → ι . 0) (Inj1 0) (λ x10 . x9 (λ x11 . 0)) 0) 0) (x5 (λ x10 . x7 (λ x11 x12 : ι → ι . x10) (setsum 0 0) 0 (Inj0 0)) (setsum 0 (Inj0 0)))) (λ x9 : ι → ι . x2 (λ x10 . x2 (λ x11 . Inj1 0) (Inj1 (Inj1 0)) (x9 (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0)) (λ x11 : ι → ι . setsum (x9 0) (x9 0))) 0 0 (λ x10 : ι → ι . x2 (λ x11 . x2 (λ x12 . x10 0) 0 (x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)) (λ x12 : ι → ι . Inj1 0)) (x6 (setsum 0 0)) (x9 (Inj0 0)) (λ x11 : ι → ι . setsum 0 0)))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : ι → ι . λ x10 . x3 (λ x11 x12 . x9 (Inj1 0)) (λ x11 x12 . λ x13 : ι → ι . x3 (λ x14 x15 . Inj0 (x0 (λ x16 : ι → ι . λ x17 . 0) (λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 . 0) (λ x16 : ι → ι . 0) 0 (λ x16 . 0) 0)) (λ x14 x15 . λ x16 : ι → ι . x16 (setsum 0 0)))) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . x6) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . x2 (λ x12 . x10 (λ x13 : ι → ι . λ x14 . setsum 0 0) (λ x13 . x1 (λ x14 : (ι → ι → ι) → ι . 0) (λ x14 . λ x15 : ι → ι . λ x16 x17 . 0) (λ x14 : (ι → ι) → ι → ι . 0))) (x10 (λ x12 : ι → ι . λ x13 . x0 (λ x14 : ι → ι . λ x15 . 0) (λ x14 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x15 . 0) (λ x14 : ι → ι . 0) 0 (λ x14 . 0) 0) (λ x12 . x10 (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0))) (x3 (λ x12 x13 . setsum 0 0) (λ x12 x13 . λ x14 : ι → ι . x2 (λ x15 . 0) 0 0 (λ x15 : ι → ι . 0))) (λ x12 : ι → ι . setsum 0 0)) (λ x10 : ι → ι . x3 (λ x11 x12 . Inj0 0) (λ x11 x12 . λ x13 : ι → ι . 0)) (x9 (x0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0) 0 (λ x11 . 0) 0) 0 (λ x10 . 0) (x1 (λ x10 : (ι → ι → ι) → ι . 0) (λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (λ x10 : (ι → ι) → ι → ι . 0)))) (λ x10 . x0 (λ x11 : ι → ι . λ x12 . x0 (λ x13 : ι → ι . λ x14 . Inj0 0) (λ x13 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x14 . 0) (λ x13 : ι → ι . Inj1 0) (x2 (λ x13 . 0) 0 0 (λ x13 : ι → ι . 0)) (λ x13 . x3 (λ x14 x15 . 0) (λ x14 x15 . λ x16 : ι → ι . 0)) 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . x9 (x11 0)) 0 (λ x11 . 0) (x3 (λ x11 x12 . setsum 0 0) (λ x11 x12 . λ x13 : ι → ι . setsum 0 0))) (Inj0 x6)) (Inj0 x7) (λ x9 . x2 (λ x10 . 0) 0 0 (λ x10 : ι → ι . setsum (x0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . x10 0) (x10 0) (λ x11 . x10 0) (Inj0 0)) (Inj0 0))) 0 = setsum (setsum (x4 (λ x9 : (ι → ι) → ι . x3 (λ x10 x11 . x7) (λ x10 x11 . λ x12 : ι → ι . Inj0 0)) 0) (setsum (x0 (λ x9 : ι → ι . λ x10 . x3 (λ x11 x12 . 0) (λ x11 x12 . λ x13 : ι → ι . 0)) (λ x9 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x10 . 0) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0) x6 (λ x9 . x9) (x1 (λ x9 : (ι → ι → ι) → ι . 0) (λ x9 . λ x10 : ι → ι . λ x11 x12 . 0) (λ x9 : (ι → ι) → ι → ι . 0))) (Inj1 (x5 0)))) (x1 (λ x9 : (ι → ι → ι) → ι . x5 (x9 (λ x10 x11 . x1 (λ x12 : (ι → ι → ι) → ι . 0) (λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (λ x12 : (ι → ι) → ι → ι . 0)))) (λ x9 . λ x10 : ι → ι . λ x11 x12 . x10 (Inj1 (x10 0))) (λ x9 : (ι → ι) → ι → ι . setsum x6 (setsum (x9 (λ x10 . 0) 0) (x0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 . 0) (λ x10 : ι → ι . 0) 0 (λ x10 . 0) 0))))) ⟶ False (proof)
Theorem b6398.. : ∀ 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 (proof)
Theorem eaa86.. : ∀ x0 : (ι → ι → ι → ι) → (ι → ι → (ι → ι) → ι) → ι . ∀ x1 : (((ι → ι → ι → ι) → ι) → ((ι → ι → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι → ι . ∀ x3 : (ι → ι → (ι → ι → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι → ι . (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι → ι . x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . setsum 0 (x3 (λ x14 x15 . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . x18) (setsum (x1 (λ x14 : (ι → ι → ι → ι) → ι . λ x15 : (ι → ι → ι) → ι . 0) 0)) (x2 (λ x14 . x14) (x2 (λ x14 . 0) 0 0) (x2 (λ x14 . 0) 0 0)))) (λ x9 . x5) (x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 x15 x16 . Inj1 (x2 (λ x17 . 0) 0 0)) (λ x14 x15 . λ x16 : ι → ι . 0)) (λ x9 . setsum (x1 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 : (ι → ι → ι) → ι . x0 (λ x12 x13 x14 . 0) (λ x12 x13 . λ x14 : ι → ι . 0)) x5) (x1 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 : (ι → ι → ι) → ι . 0) (Inj0 0))) x5) = x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . Inj1) (λ x9 . setsum 0 (Inj0 x9)) (x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0) x6)) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x11 (Inj0 (setsum (x0 (λ x14 x15 x16 . 0) (λ x14 x15 . λ x16 : ι → ι . 0)) 0)) (setsum 0 (x12 (x2 (λ x14 . 0) 0 0)))) (λ x9 . x9) (x4 (Inj1 (x2 (λ x9 . 0) 0 0)) (λ x9 : ι → ι . x6) (Inj1 x7) (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . x7) (x4 x7 (λ x9 : ι → ι . x0 (λ x10 x11 x12 . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (Inj1 0) (setsum 0 0)))) = x4 (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . Inj0 (x1 (λ x11 : (ι → ι → ι → ι) → ι . λ x12 : (ι → ι → ι) → ι . x11 (λ x13 x14 x15 . 0)) (Inj0 0))) 0) (λ x9 : ι → ι . Inj1 (x0 (λ x10 x11 x12 . x2 (λ x13 . 0) (setsum 0 0) 0) (λ x10 x11 . λ x12 : ι → ι . x11))) x6 (setsum (x4 (x0 (λ x9 x10 x11 . 0) (λ x9 x10 . λ x11 : ι → ι . 0)) (λ x9 : ι → ι . Inj0 x5) (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . 0) (x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . 0) 0)) (x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . setsum 0 0) (λ x9 . x5) 0)) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 . x9) (Inj1 0) (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . x7) (x2 (λ x9 . x6) (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . 0) (setsum 0 0)) (x0 (λ x9 x10 x11 . x11) (λ x9 x10 . λ x11 : ι → ι . x7)))) = Inj0 (x4 (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 . x9) x4 (Inj1 (setsum (x5 x7) (x0 (λ x9 x10 x11 . setsum 0 0) (λ x9 x10 . λ x11 : ι → ι . 0)))) = x4) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . x3 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . Inj0 0) (λ x11 . 0) (Inj1 (Inj1 (x1 (λ x11 : (ι → ι → ι → ι) → ι . λ x12 : (ι → ι → ι) → ι . 0) 0)))) 0 = x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj1 0) (λ x9 . setsum (x1 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 : (ι → ι → ι) → ι . x0 (λ x12 x13 x14 . 0) (λ x12 x13 . λ x14 : ι → ι . setsum 0 0)) (setsum (x2 (λ x10 . 0) 0 0) x6)) (Inj0 (setsum 0 x6))) (setsum 0 (x3 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj1 (x11 0 0)) (λ x9 . x1 (λ x10 : (ι → ι → ι → ι) → ι . λ x11 : (ι → ι → ι) → ι . 0) 0) (Inj0 (x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . 0) 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . x1 (λ x9 : (ι → ι → ι → ι) → ι . λ x10 : (ι → ι → ι) → ι . x9 (λ x11 x12 x13 . Inj1 (x2 (λ x14 . 0) (Inj0 0) (x2 (λ x14 . 0) 0 0)))) (Inj0 (x0 (λ x9 x10 . x3 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x3 (λ x16 x17 . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 . 0) 0) (λ x11 . x10)) (λ x9 x10 . λ x11 : ι → ι . x9))) = setsum (x0 (λ x9 x10 x11 . 0) (λ x9 x10 . λ x11 : ι → ι . setsum (x0 (λ x12 x13 x14 . x1 (λ x15 : (ι → ι → ι → ι) → ι . λ x16 : (ι → ι → ι) → ι . 0) 0) (λ x12 x13 . λ x14 : ι → ι . 0)) 0)) 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x7 . x0 (λ x9 x10 x11 . 0) (λ x9 x10 . λ x11 : ι → ι . x10) = x6 (λ x9 : (ι → ι) → ι . setsum (x5 (λ x10 x11 . x11)) 0) x4) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 x7 . x0 (λ x9 x10 x11 . x7) (λ x9 x10 . λ x11 : ι → ι . Inj0 (x0 (λ x12 x13 x14 . setsum 0 (Inj0 0)) (λ x12 x13 . λ x14 : ι → ι . x13))) = x7) ⟶ False (proof)
Theorem bbce6.. : ∀ x0 : (ι → ((ι → ι) → (ι → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x1 : ((ι → (ι → ι) → ι) → ι → ι) → ι → ι . ∀ x2 : (((ι → ι) → ι) → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι → ι) → (ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → ι . λ x10 . x6) (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . Inj0 (x10 (λ x14 . Inj0 0) (λ x14 . 0)))) = setsum (setsum 0 (x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . setsum (x3 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)) x7) (x3 (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)) (λ x9 . x1 (λ x10 : ι → (ι → ι) → ι . λ x11 . 0) 0)))) (Inj0 x4)) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . setsum 0 (x3 (λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → ι . x2 (λ x13 : (ι → ι) → ι . 0) 0) x9) (λ x10 . x1 (λ x11 : ι → (ι → ι) → ι . λ x12 . Inj1 0) x7))) = x5) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι) → ι . x5 (λ x10 . λ x11 : ι → ι . x9 (λ x12 . 0)) (x2 (λ x10 : (ι → ι) → ι . x7) 0) (λ x10 . 0) (Inj0 x7)) (Inj1 (x6 x4 (x6 (x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . 0) 0) (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . 0) 0) (x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . 0) 0)) 0)) = Inj1 (x5 (λ x9 . λ x10 : ι → ι . x7) (Inj1 (Inj0 (setsum 0 0))) (λ x9 . 0) 0)) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x2 (λ x9 : (ι → ι) → ι . x3 (λ x10 : ι → ι . x10) (λ x10 . x7 (setsum (x1 (λ x11 : ι → (ι → ι) → ι . λ x12 . 0) 0) 0) 0 (λ x11 . Inj0 (x2 (λ x12 : (ι → ι) → ι . 0) 0)) (x3 (λ x11 : ι → ι . λ x12 . Inj0 0) (λ x11 . 0)))) (setsum 0 0) = x3 (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 : (ι → ι) → ι . setsum (x0 (λ x12 . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 : ι → ι . λ x16 . 0) 0) (x2 (λ x12 : (ι → ι) → ι . 0) 0)) (setsum (x0 (λ x11 . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 : ι → ι . λ x15 . 0) 0) (x1 (λ x11 : ι → (ι → ι) → ι . λ x12 . 0) 0))) (x0 (λ x11 . λ x12 : (ι → ι) → (ι → ι) → ι . λ x13 x14 : ι → ι . λ x15 . 0) (setsum (setsum 0 0) (x2 (λ x11 : (ι → ι) → ι . 0) 0)))) (λ x9 . Inj0 (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . Inj0 (x2 (λ x11 : (ι → ι) → ι . 0) (Inj0 0))) (setsum (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . Inj1 0) 0) (Inj0 0)) = x5 (λ x9 : ι → ι → ι . 0) (λ x9 x10 . 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 . x2 (λ x13 : (ι → ι) → ι . setsum 0 (x2 (λ x14 : (ι → ι) → ι . 0) 0)) (x2 (λ x13 : (ι → ι) → ι . 0) x10)) (λ x11 . setsum (Inj1 0) (x0 (λ x12 . λ x13 : (ι → ι) → (ι → ι) → ι . λ x14 x15 : ι → ι . λ x16 . x13 (λ x17 . 0) (λ x17 . 0)) (x9 0 (λ x12 . 0))))) (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . x2 (λ x14 : (ι → ι) → ι . Inj0 (Inj0 0)) (Inj1 (setsum 0 0))) (x4 (Inj1 0))) = x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . x12 (x10 (λ x14 . x14) (λ x14 . 0))) (Inj0 (setsum (Inj0 (x3 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0))) (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . x2 (λ x14 : (ι → ι) → ι . 0) 0) (setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι . ∀ x5 : ι → (ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . x11 (setsum x13 (x3 (λ x14 : ι → ι . λ x15 . x3 (λ x16 : ι → ι . λ x17 . 0) (λ x16 . 0)) (λ x14 . x12 0)))) (x4 (λ x9 : ι → ι → ι . 0) (setsum 0 0)) = setsum 0 (setsum (x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . 0) 0) 0)) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : (ι → ι) → (ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . 0) (x3 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0)) = setsum (x1 (λ x9 : ι → (ι → ι) → ι . λ x10 . 0) 0) 0) ⟶ False (proof)
Theorem d61cb.. : ∀ 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 → ι) → ι . ∀ x2 : (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 x6 x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι → ι . λ x11 : (ι → ι) → ι → ι . setsum (x9 (λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . 0) (setsum 0 0))) (setsum (Inj0 0) (x0 (λ x12 : ι → (ι → ι → ι) → ι . 0) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . 0) 0))) (x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . Inj0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι → ι . λ x13 : (ι → ι) → ι → ι . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . 0) 0) x10 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x3 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι → ι . λ x15 : (ι → ι) → ι → ι . 0) 0 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0) 0) (λ x11 : ι → ι . Inj1 0) x10)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . x0 (λ x11 : ι → (ι → ι → ι) → ι . 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . 0) (setsum (Inj1 0) (setsum 0 0)))) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x12) (x10 0)) (λ x9 : ι → ι . x7) 0 = x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . Inj0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x12 : ι → ι → ι → ι . λ x13 : (ι → ι) → ι → ι . 0) 0 (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . Inj1 (x3 (λ x13 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x14 : ι → ι → ι → ι . λ x15 : (ι → ι) → ι → ι . 0) 0 (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x13 : ι → ι . 0) 0)) (λ x11 : ι → ι . x1 (λ x12 : (ι → ι → ι → ι) → ι → ι . λ x13 . x10) (λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 . x13)) (x9 (λ x11 x12 x13 . x1 (λ x14 : (ι → ι → ι → ι) → ι → ι . λ x15 . 0) (λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 . 0)) 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . x1 (λ x11 : (ι → ι → ι → ι) → ι → ι . λ x12 . x10) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 . x11 (λ x13 x14 . x3 (λ x15 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x16 : ι → ι → ι → ι . λ x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . 0) (λ x15 : ι → ι . setsum 0 0) (Inj1 0)) (λ x13 . 0)))) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι → ι . λ x11 : (ι → ι) → ι → ι . 0) 0 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . Inj1 (x0 (λ x11 : ι → (ι → ι → ι) → ι . x0 (λ x12 : ι → (ι → ι → ι) → ι . x2 (λ x13 x14 x15 . λ x16 : ι → ι . λ x17 . 0) 0) (λ x12 : ((ι → ι) → ι) → ι → ι → ι . x10 0) 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . 0) 0)) (λ x9 : ι → ι . 0) (Inj0 0) = x4) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι . x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . setsum 0 (setsum (setsum 0 (setsum 0 0)) x10)) 0 = x5 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . x16) 0) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0) = x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . Inj1 (x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . setsum (x3 (λ x19 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x20 : ι → ι → ι → ι . λ x21 : (ι → ι) → ι → ι . 0) 0 (λ x19 : (ι → ι) → ι → ι . λ x20 : ι → ι . 0) (λ x19 : ι → ι . 0) 0) (x1 (λ x19 : (ι → ι → ι → ι) → ι → ι . λ x20 . 0) (λ x19 : (ι → ι → ι) → (ι → ι) → ι . λ x20 . 0))) (x12 (Inj0 0)))) x6) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x15) (Inj1 (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . 0) (x9 (λ x11 x12 x13 . 0) 0)))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . 0) = setsum (x0 (λ x9 : ι → (ι → ι → ι) → ι . x5) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . Inj1 x7) (Inj1 (x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . x9 (λ x11 x12 x13 . 0) 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . x6)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . Inj0 (x1 (λ x11 : (ι → ι → ι → ι) → ι → ι . λ x12 . Inj1 (Inj1 0)) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 . 0))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . 0) = x4 (setsum (Inj0 0) (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι → ι) → ι . x0 (λ x9 : ι → (ι → ι → ι) → ι . setsum (setsum 0 (x7 (λ x10 x11 x12 . x11))) (x9 0 (λ x10 x11 . Inj0 (Inj0 0)))) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . setsum x6 0) x6 = x6) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι → ι → ι . ∀ x7 . x0 (λ x9 : ι → (ι → ι → ι) → ι . x1 (λ x10 : (ι → ι → ι → ι) → ι → ι . λ x11 . x9 0 (λ x12 x13 . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 . 0)) (λ x9 : ((ι → ι) → ι) → ι → ι → ι . Inj1 (Inj0 x7)) (setsum (x3 (λ x9 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x10 : ι → ι → ι → ι . λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : (ι → ι → ι → ι) → ι → ι . λ x13 . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . 0) 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 . x11 (λ x14 . 0) 0)) (x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . x9 (λ x11 x12 x13 . 0) 0) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x1 (λ x11 : (ι → ι → ι → ι) → ι → ι . λ x12 . setsum 0 0) (λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 . Inj0 0)) (λ x9 : ι → ι . Inj1 (setsum 0 0)) 0) (Inj1 x4)) = x1 (λ x9 : (ι → ι → ι → ι) → ι → ι . λ x10 . x6 (λ x11 . setsum (x3 (λ x12 : (((ι → ι) → ι → ι) → ι → ι) → ι . λ x13 : ι → ι → ι → ι . λ x14 : (ι → ι) → ι → ι . x14 (λ x15 . 0) 0) (x1 (λ x12 : (ι → ι → ι → ι) → ι → ι . λ x13 . 0) (λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 . 0)) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x12 : ι → ι . setsum 0 0) (x2 (λ x12 x13 x14 . λ x15 : ι → ι . λ x16 . 0) 0))) 0 (x0 (λ x11 : ι → (ι → ι → ι) → ι . 0) (λ x11 : ((ι → ι) → ι) → ι → ι → ι . x11 (λ x12 : ι → ι . 0) (setsum 0 0) (Inj1 0)) (setsum (Inj1 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . 0) 0)))) (λ x9 : (ι → ι → ι) → (ι → ι) → ι . λ x10 . Inj0 (setsum (Inj1 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . Inj0 0) 0)))) ⟶ False (proof)
Theorem 594e6.. : ∀ 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) → (ι → ι) → ι . ∀ x1 : (((ι → ι) → (ι → ι → ι) → ι) → ι → ι → (ι → ι) → ι) → ι → ι → ι → (ι → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → ι → ι) → ((((ι → ι) → ι) → ι → ι) → ι) → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 x10 . 0) (λ x9 : ((ι → ι) → ι) → ι → ι . x3 (λ x10 x11 . setsum 0 (x7 0)) (λ x10 : ((ι → ι) → ι) → ι → ι . x10 (λ x11 : ι → ι . setsum (setsum 0 0) (x7 0)) (Inj1 (setsum 0 0)))) = x3 (λ x9 x10 . Inj0 (setsum x6 (setsum 0 x10))) (λ x9 : ((ι → ι) → ι) → ι → ι . setsum 0 (x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . x12 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . x2 (λ x13 . x0 (λ x14 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 : ι → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 . 0) (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0)) (Inj1 0)) (λ x10 . Inj1 (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . 0) 0 0 0 (λ x11 . 0) 0)) (λ x10 : ι → ι . λ x11 . Inj0 (x7 0)) (λ x10 . x7 0)))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι → ι . x3 (λ x9 x10 . setsum (x0 (λ x11 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . setsum 0 0) (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . x11)) x9) (λ x9 : ((ι → ι) → ι) → ι → ι . setsum (x9 (λ x10 : ι → ι . x2 (λ x11 . Inj0 0) (x3 (λ x11 x12 . 0) (λ x11 : ((ι → ι) → ι) → ι → ι . 0))) (x2 (λ x10 . x0 (λ x11 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)) (Inj0 0))) 0) = x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι) → ι → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 . x2 (λ x10 . x7) 0) (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . setsum (x9 (λ x12 x13 x14 . 0) (λ x12 : ι → ι . x3 (λ x13 x14 . 0) (λ x13 : ((ι → ι) → ι) → ι → ι . 0)) (x2 (λ x12 . 0) 0)) (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . setsum 0 0) 0 0 (setsum 0 0) (λ x12 . x12) 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 . 0) (Inj0 0)) (λ x9 . 0) (λ x9 : ι → ι . x1 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . 0) x7 (x9 0) 0 (λ x10 . 0)) (λ x9 . setsum (x3 (λ x10 x11 . x9) (λ x10 : ((ι → ι) → ι) → ι → ι . setsum 0 0)) (Inj0 0))) = Inj1 (x4 (x5 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . 0) 0 0 0 (λ x13 . 0) 0) (setsum 0 0) 0 (Inj1 0) (λ x9 . x6 0 0) 0) (λ x9 . x9) 0 (x4 (x4 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . x2 (λ x9 . x1 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . x3 (λ x18 x19 . x17 0) (λ x18 : ((ι → ι) → ι) → ι → ι . x0 (λ x19 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x20 : ι → ι → ι → ι . λ x21 : ι → ι . 0) (λ x19 : ι → ι . λ x20 . λ x21 : ι → ι . 0) (λ x19 . 0) (λ x19 : ι → ι . λ x20 . 0) (λ x19 . 0))) (setsum (x10 (λ x14 . 0) (λ x14 x15 . 0)) (Inj1 0)) (setsum (x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . 0) 0 0 0 (λ x14 . 0) 0) (x3 (λ x14 x15 . 0) (λ x14 : ((ι → ι) → ι) → ι → ι . 0))) x12 (λ x14 . setsum x11 0) (x1 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . Inj1 0) x11 (setsum 0 0) (setsum 0 0) (λ x14 . 0) x11)) (x5 (Inj1 0)) (setsum 0 (x3 (λ x10 x11 . x9) (λ x10 : ((ι → ι) → ι) → ι → ι . 0))) 0 (λ x10 . 0) (x3 (λ x10 x11 . x9) (λ x10 : ((ι → ι) → ι) → ι → ι . 0))) (x3 (λ x9 x10 . x6) (λ x9 : ((ι → ι) → ι) → ι → ι . x2 (λ x10 . x10) (setsum (x7 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0) 0))) = x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 0) x6 (x5 (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x3 (λ x12 x13 . x0 (λ x14 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 : ι → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 . 0) (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0)) (λ x12 : ((ι → ι) → ι) → ι → ι . 0)) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (setsum 0 0) (x3 (λ x12 x13 . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . 0))) (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 . x2 (λ x11 . Inj1 0) (setsum 0 0)) (λ x9 . Inj1 (setsum 0 0)))) (setsum (Inj1 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x10) 0 0 (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0) (λ x9 . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0)) (λ x9 . x9) (x3 (λ x9 x10 . 0) (λ x9 : ((ι → ι) → ι) → ι → ι . 0)))) 0) (λ x9 . Inj1 0) (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x7 (λ x12 : ι → ι → ι . λ x13 : ι → ι . setsum x11) (x9 (Inj1 0) (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0))) 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x9 (λ x13 . x10) (λ x13 x14 . x11)) (x3 (λ x9 x10 . x2 (λ x11 . 0) (x3 (λ x11 x12 . x0 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0) (λ x13 . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0)) (λ x11 : ((ι → ι) → ι) → ι → ι . x3 (λ x12 x13 . 0) (λ x12 : ((ι → ι) → ι) → ι → ι . 0)))) (λ x9 : ((ι → ι) → ι) → ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x7))) (x3 (λ x9 x10 . x3 (λ x11 x12 . x11) (λ x11 : ((ι → ι) → ι) → ι → ι . x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . Inj1 0) (x0 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x13 : ι → ι → ι → ι . λ x14 : ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0) (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)) (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0) (x2 (λ x12 . 0) 0) (λ x12 . Inj0 0) 0)) (λ x9 : ((ι → ι) → ι) → ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . Inj1 (Inj1 0)))) x7 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0)) (x2 (λ x9 . 0) x7) = setsum (x3 (λ x9 x10 . x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . setsum 0 (setsum 0 0)) 0 (setsum x10 0) x9 (λ x11 . x11) (setsum (Inj0 0) 0)) (λ x9 : ((ι → ι) → ι) → ι → ι . setsum 0 (Inj0 0))) (Inj1 (Inj0 (x6 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x2 (λ x13 . setsum x10 x10) (x0 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 : ι → ι . x15 (x3 (λ x16 x17 . 0) (λ x16 : ((ι → ι) → ι) → ι → ι . 0))) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . x1 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . λ x17 x18 . λ x19 : ι → ι . x18) (x1 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . λ x17 x18 . λ x19 : ι → ι . 0) 0 0 0 (λ x16 . 0) 0) (Inj0 0) (x12 0) (λ x16 . 0) 0) (λ x13 . setsum (x2 (λ x14 . 0) 0) 0) (λ x13 : ι → ι . λ x14 . x14) (λ x13 . Inj1 x10))) (x5 (x3 (λ x9 x10 . x2 (λ x11 . 0) 0) (λ x9 : ((ι → ι) → ι) → ι → ι . x2 (λ x10 . setsum 0 0) (x2 (λ x10 . 0) 0)))) (Inj0 (x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : (ι → ι) → (ι → ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . Inj0 0) 0 (x0 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0) (λ x13 . 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . 0)) (setsum 0 0) (λ x13 . 0) 0) (Inj1 (setsum 0 0)) (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x2 (λ x12 . 0) 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0) (λ x9 . Inj0 0) (λ x9 : ι → ι . λ x10 . x6) (λ x9 . Inj0 0)) (Inj1 (Inj1 0)) (λ x9 . x7) (Inj0 0))) (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x9 (λ x12 x13 x14 . 0) (λ x12 : ι → ι . Inj1 0) (x3 (λ x12 x13 . x10 0 0 0) (λ x12 : ((ι → ι) → ι) → ι → ι . 0))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 x13 . x2 (λ x14 . x0 (λ x15 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x16 : ι → ι → ι → ι . λ x17 : ι → ι . 0) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . 0) (λ x15 . 0) (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0)) 0) (λ x12 : ((ι → ι) → ι) → ι → ι . x9 0)) (λ x9 . x7) (λ x9 : ι → ι . λ x10 . setsum (x1 (λ x11 : (ι → ι) → (ι → ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . x3 (λ x15 x16 . 0) (λ x15 : ((ι → ι) → ι) → ι → ι . 0)) (setsum 0 0) (x0 (λ x11 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0) (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0)) (x3 (λ x11 x12 . 0) (λ x11 : ((ι → ι) → ι) → ι → ι . 0)) (λ x11 . setsum 0 0) 0) (x9 (setsum 0 0))) (λ x9 . 0)) (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . x10 (λ x13 x14 x15 . x14) (λ x13 : ι → ι . setsum (x0 (λ x14 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 : ι → ι . 0) (λ x14 : ι → ι . λ x15 . λ x16 : ι → ι . 0) (λ x14 . 0) (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0)) (Inj0 0)) 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . Inj1 (setsum 0 (x10 0))) (λ x10 . setsum 0 (Inj0 (setsum 0 0))) (λ x10 : ι → ι . λ x11 . x10 0) (λ x10 . 0)) (x5 (setsum (setsum (setsum 0 0) (setsum 0 0)) x7)) = x5 (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x7) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x0 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x13 : ι → ι → ι → ι . λ x14 : ι → ι . x13 (x14 0) (x0 (λ x15 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x16 : ι → ι → ι → ι . λ x17 : ι → ι . 0) (λ x15 : ι → ι . λ x16 . λ x17 : ι → ι . 0) (λ x15 . 0) (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0)) (x1 (λ x15 : (ι → ι) → (ι → ι → ι) → ι . λ x16 x17 . λ x18 : ι → ι . 0) 0 0 0 (λ x15 . 0) 0)) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . Inj0 0) (λ x12 . setsum (Inj1 0) 0) (λ x12 : ι → ι . λ x13 . x12 (Inj0 0)) (λ x12 . x9 0)) (λ x9 . 0) (λ x9 : ι → ι . λ x10 . x9 (Inj0 0)) (λ x9 . x6))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x7) (λ x9 . Inj0 0) (λ x9 : ι → ι . λ x10 . Inj0 0) (λ x9 . x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 . Inj1 (Inj0 0)) (x12 (setsum 0 0))) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) (λ x10 . x9) (λ x10 : ι → ι . λ x11 . setsum (x3 (λ x12 x13 . x10 0) (λ x12 : ((ι → ι) → ι) → ι → ι . x9)) (setsum 0 (setsum 0 0))) (λ x10 . x3 (λ x11 x12 . Inj0 (setsum 0 0)) (λ x11 : ((ι → ι) → ι) → ι → ι . x10))) = setsum x4 (setsum (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . Inj0 (x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 0 0 (λ x12 . 0) 0)) (λ x9 . x7) (λ x9 : ι → ι . λ x10 . setsum (Inj0 0) (x6 0)) (λ x9 . 0)) (x2 (λ x9 . setsum (Inj0 0) (x0 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0) (λ x10 . 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0))) (x3 (λ x9 x10 . x6 0) (λ x9 : ((ι → ι) → ι) → ι → ι . setsum 0 0))))) ⟶ (∀ x4 : ((ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . x1 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . Inj1 (x15 x13)) (Inj0 (setsum (x2 (λ x12 . 0) 0) 0)) 0 0 (λ x12 . x2 (λ x13 . setsum (setsum 0 0) (x2 (λ x14 . 0) 0)) 0) x7) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (Inj1 (Inj0 (x9 0))) 0) (λ x9 . setsum 0 (setsum x7 (Inj1 (x1 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . 0) 0 0 0 (λ x10 . 0) 0)))) (λ x9 : ι → ι . λ x10 . x6) (λ x9 . x6) = x1 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x12 (x3 (λ x13 x14 . Inj1 0) (λ x13 : ((ι → ι) → ι) → ι → ι . x11))) (setsum (setsum 0 x7) (Inj1 x6)) (Inj1 (Inj0 (setsum (x0 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0) (λ x9 . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0)) (setsum 0 0)))) (Inj0 x7) (λ x9 . Inj0 0) (setsum 0 (x4 (λ x9 : ι → ι . x6) (λ x9 : ι → ι . 0)))) ⟶ False (proof)
Theorem 0f506.. : ∀ x0 : (ι → (((ι → ι) → ι) → ι) → ι → ι → ι → ι) → ι → ι . ∀ x1 : (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) → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 : ι → ι . x3 (λ x9 x10 . x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x11 0 (λ x12 : ι → ι . 0) (λ x12 . x3 (λ x13 x14 . x3 (λ x15 x16 . 0) (λ x15 : ι → ι → ι . λ x16 : (ι → ι) → ι → ι . 0)) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι → ι . setsum 0 0))) (λ x11 x12 . Inj0 0)) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι → ι . x9 0 (x10 (λ x11 . setsum (x10 (λ x12 . 0) 0) 0) (x7 (x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 x12 . 0))))) = Inj0 0) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 x10 . x1 (λ x11 . x7) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . x2 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x12 x13 . x1 (λ x14 . x1 (λ x15 . 0) (λ x15 : ι → ι . λ x16 . 0) (λ x15 . 0) (λ x15 x16 . 0)) (λ x14 : ι → ι . λ x15 . x0 (λ x16 . λ x17 : ((ι → ι) → ι) → ι . λ x18 x19 x20 . 0) 0) (λ x14 . x0 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 x18 x19 . 0) 0) (λ x14 x15 . Inj0 0))) (λ x11 x12 . 0)) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι → ι . setsum (setsum (x3 (λ x11 x12 . Inj1 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 x14 . 0) (λ x13 : ι → ι → ι . λ x14 : (ι → ι) → ι → ι . 0))) (x3 (λ x11 x12 . x11) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι → ι . 0))) (setsum (x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . Inj0 0) (λ x11 x12 . setsum 0 0)) (setsum 0 (x6 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 . 0) 0)))) = x1 (λ x9 . x6 (λ x10 : ι → ι . x1 (λ x11 . x3 (λ x12 x13 . Inj0 0) (λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι → ι . x10 0)) (λ x11 : ι → ι . λ x12 . x10 (setsum 0 0)) (λ x11 . setsum (x0 (λ x12 . λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 x16 . 0) 0) (x2 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x12 x13 . 0))) (λ x11 x12 . 0)) (λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . setsum x7 (x11 0 (λ x12 : ι → ι . 0) (λ x12 . 0))) (λ x11 x12 . x10 (Inj1 0))) (λ x10 . 0) (x2 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 x11 . Inj0 0))) (λ x9 : ι → ι . λ x10 . setsum (Inj1 0) (setsum 0 (x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 x15 . x15) (x1 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) (λ x11 x12 . 0))))) (λ x9 . x9) (λ x9 x10 . x9)) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι . setsum (x2 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι . Inj0 (x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 x15 . 0) 0)) (λ x10 x11 . 0)) (x2 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι . setsum (setsum 0 0) (x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 x12 . 0))) (λ x10 x11 . x1 (λ x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 x17 . 0) 0) (λ x12 : ι → ι . λ x13 . setsum 0 0) (λ x12 . 0) (λ x12 x13 . 0)))) (λ x9 . setsum (Inj1 0)) = Inj0 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 x13 . x12) 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x5) (λ x9 x10 . 0) = setsum (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 x13 . x2 (λ x14 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x14 x12 (λ x15 : ι → ι . Inj1 0) (λ x15 . Inj1 0)) (λ x14 x15 . x2 (λ x16 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x15) (λ x16 x17 . 0))) (setsum (setsum (Inj0 0) (Inj0 0)) 0)) (x7 (Inj1 (x4 0 0)) (λ x9 . x2 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 x11 . x2 (λ x12 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x13 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 x14 . 0)) (λ x12 x13 . x11))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x1 (λ x9 . x5 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 x14 . x12) 0) (λ x10 . x3 (λ x11 x12 . 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι → ι . setsum (x2 (λ x13 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x13 x14 . 0)) (setsum 0 0)))) (λ x9 : ι → ι . λ x10 . x1 (λ x11 . setsum (Inj0 (Inj1 0)) 0) (λ x11 : ι → ι . λ x12 . setsum 0 (Inj1 x12)) (λ x11 . x9 (setsum (x1 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0) (λ x12 x13 . 0)) 0)) (λ x11 x12 . Inj1 (x1 (λ x13 . Inj1 0) (λ x13 : ι → ι . λ x14 . x12) (λ x13 . x3 (λ x14 x15 . 0) (λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι → ι . 0)) (λ x13 x14 . x0 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 x18 x19 . 0) 0)))) (λ x9 . x3 (λ x10 x11 . x7) (λ x10 : ι → ι → ι . λ x11 : (ι → ι) → ι → ι . Inj0 (Inj1 (setsum 0 0)))) (λ x9 x10 . x10) = Inj0 (x3 (λ x9 x10 . Inj0 x7) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι → ι . 0))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 x14 . 0) (setsum 0 0)) (λ x9 : ι → ι . λ x10 . Inj1 (x9 (x7 (Inj0 0)))) (λ x9 . x9) (λ x9 x10 . 0) = x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 x13 . setsum (setsum x11 x11) (setsum (x3 (λ x14 x15 . x3 (λ x16 x17 . 0) (λ x16 : ι → ι → ι . λ x17 : (ι → ι) → ι → ι . 0)) (λ x14 : ι → ι → ι . λ x15 : (ι → ι) → ι → ι . x2 (λ x16 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x16 x17 . 0))) (x1 (λ x14 . 0) (λ x14 : ι → ι . λ x15 . x2 (λ x16 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x16 x17 . 0)) (λ x14 . x14) (λ x14 x15 . x1 (λ x16 . 0) (λ x16 : ι → ι . λ x17 . 0) (λ x16 . 0) (λ x16 x17 . 0))))) (Inj0 (x3 (λ x9 x10 . Inj0 (x3 (λ x11 x12 . 0) (λ x11 : ι → ι → ι . λ x12 : (ι → ι) → ι → ι . 0))) (λ x9 : ι → ι → ι . λ x10 : (ι → ι) → ι → ι . Inj0 (Inj1 0))))) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 x13 . Inj0 x11) 0 = x5 (x4 (setsum 0 (x2 (λ x9 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x10 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x10 x11 . 0)) (λ x9 x10 . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 x15 . 0) 0))) (λ x9 . x5 x7 x9 (x1 (λ x10 . setsum 0 0) (λ x10 : ι → ι . λ x11 . x3 (λ x12 x13 . 0) (λ x12 : ι → ι → ι . λ x13 : (ι → ι) → ι → ι . 0)) (λ x10 . x2 (λ x11 : ι → ((ι → ι) → ι) → (ι → ι) → ι . 0) (λ x11 x12 . 0)) (λ x10 x11 . 0)) x7)) 0 x6 (x1 (λ x9 . setsum 0 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) (λ x9 x10 . x10))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 x13 . 0) 0 = x7 (λ x9 . 0)) ⟶ False (proof)
Theorem 3976e.. : ∀ x0 : (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 . ∀ 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 . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . setsum x7 0) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . x7) = x7) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 . x2 (λ x10 . x7) (λ x10 : ι → ι . x3 (λ x11 : ι → ι . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0) x7) (λ x11 : ι → (ι → ι) → ι → ι . setsum 0 (Inj0 0))) (λ x10 x11 . x2 (λ x12 . x2 (λ x13 . x11) (λ x13 : ι → ι . setsum 0 0) (λ x13 x14 . 0) (λ x13 x14 . 0) 0) (λ x12 : ι → ι . Inj1 0) (λ x12 x13 . 0) (λ x12 x13 . x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . x0 (λ x19 x20 . λ x21 : ι → ι → ι . λ x22 . 0) 0 (λ x19 : ι → ι . 0)) (x0 (λ x14 x15 . λ x16 : ι → ι → ι . λ x17 . 0) 0 (λ x14 : ι → ι . 0))) x7) (λ x10 x11 . Inj0 (setsum x9 (setsum 0 0))) x7) (λ x9 : ι → ι . x9 (Inj1 (setsum 0 (setsum 0 0)))) (λ x9 x10 . 0) (λ x9 x10 . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . 0) x7 (λ x11 : ι → ι . 0)) (x5 (λ x9 x10 : ι → ι . setsum (x1 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . Inj1 0) (x9 0)) x7)) = x5 (λ x9 x10 : ι → ι . x9 (Inj1 (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ((ι → ι) → ι) → ι → ι . x2 (λ x9 . x2 (λ x10 . x10) (λ x10 : ι → ι . Inj0 (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . x13 0 0) (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x11 : ι → ι . 0)) (λ x11 : ι → ι . Inj1 0))) (λ x10 x11 . 0) (λ x10 x11 . x2 (λ x12 . 0) (λ x12 : ι → ι . x10) (λ x12 x13 . x0 (λ x14 x15 . λ x16 : ι → ι → ι . λ x17 . Inj1 0) x13 (λ x14 : ι → ι . 0)) (λ x12 x13 . 0) 0) (Inj1 0)) (λ x9 : ι → ι . Inj1 0) (λ x9 x10 . x2 (λ x11 . x11) (λ x11 : ι → ι . 0) (λ x11 x12 . x2 (λ x13 . 0) (λ x13 : ι → ι . x12) (λ x13 x14 . x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 . x15) (x2 (λ x15 . 0) (λ x15 : ι → ι . 0) (λ x15 x16 . 0) (λ x15 x16 . 0) 0) (λ x15 : ι → ι . x15 0)) (λ x13 x14 . x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 . x18) 0 (λ x15 : ι → ι . x1 (λ x16 x17 . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0) 0)) x11) (λ x11 x12 . 0) 0) (λ x9 x10 . x9) (x6 (setsum 0 (setsum (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x9 : ι → ι . 0)) 0))) = x2 (λ x9 . Inj0 (x2 (λ x10 . x10) (λ x10 : ι → ι . x2 (λ x11 . x9) (λ x11 : ι → ι . x10 0) (λ x11 x12 . x11) (λ x11 x12 . x12) 0) (λ x10 x11 . Inj1 0) (λ x10 x11 . setsum 0 (x2 (λ x12 . 0) (λ x12 : ι → ι . 0) (λ x12 x13 . 0) (λ x12 x13 . 0) 0)) 0)) (λ x9 : ι → ι . setsum 0 0) (λ x9 x10 . setsum 0 (x3 (λ x11 : ι → ι . x10) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 . setsum 0 0) (Inj0 0) (λ x12 : ι → ι . x11 0 (λ x13 . 0) 0)))) (λ x9 x10 . x7 (λ x11 . Inj0 (Inj1 0)) (λ x11 : ι → ι . Inj0 x10) 0) (x6 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . 0) (setsum (setsum 0 0) (x7 (λ x9 . 0) (λ x9 : ι → ι . 0) 0)) (λ x9 : ι → ι . 0)))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . setsum x13 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) (setsum 0 (setsum 0 0))) (setsum (x2 (λ x9 . setsum 0 0) (λ x9 : ι → ι . setsum 0 0) (λ x9 x10 . x10) (λ x9 x10 . x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x11 : ι → ι . 0)) 0) 0)) = x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 (x12 (setsum (Inj1 0) x10))) (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) x4 = setsum (setsum (x2 (λ x9 . 0) (λ x9 : ι → ι . setsum (x0 (λ x10 x11 . λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x10 : ι → ι . 0)) (x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0)) (λ x9 x10 . x9) (λ x9 x10 . Inj1 x6) (Inj1 0)) 0) 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0) (x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . 0) x12 (λ x13 : ι → ι . x11 0 0))) (x2 (λ x9 . x3 (λ x10 : ι → ι . x10 x9) (λ x10 : ι → (ι → ι) → ι → ι . x3 (λ x11 : ι → ι . x7 0 0 0) (λ x11 : ι → (ι → ι) → ι → ι . x0 (λ x12 x13 . λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x12 : ι → ι . 0)))) (λ x9 : ι → ι . Inj1 (x9 (Inj0 0))) (λ x9 x10 . x7 x10 (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . x11) (x0 (λ x11 x12 . λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x11 : ι → ι . 0)) (λ x11 : ι → ι . setsum 0 0)) 0) (λ x9 x10 . 0) (Inj1 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . Inj1 0) 0 (λ x9 : ι → ι . x9 0)))) (λ x9 : ι → ι . x5) = x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) (setsum 0 (x12 (setsum 0 0)))) (setsum x4 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : ι → ι → ι . λ x16 . x2 (λ x17 . x2 (λ x18 . x15 0 0) (λ x18 : ι → ι . setsum 0 0) (λ x18 x19 . x3 (λ x20 : ι → ι . 0) (λ x20 : ι → (ι → ι) → ι → ι . 0)) (λ x18 x19 . 0) 0) (λ x17 : ι → ι . Inj1 (setsum 0 0)) (λ x17 x18 . x15 x18 (x1 (λ x19 x20 . λ x21 : (ι → ι) → ι → ι . λ x22 : ι → ι . λ x23 . 0) 0)) (λ x17 x18 . x3 (λ x19 : ι → ι . x3 (λ x20 : ι → ι . 0) (λ x20 : ι → (ι → ι) → ι → ι . 0)) (λ x19 : ι → (ι → ι) → ι → ι . x2 (λ x20 . 0) (λ x20 : ι → ι . 0) (λ x20 x21 . 0) (λ x20 x21 . 0) 0)) 0) (x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . x15 (λ x18 . setsum 0 0) 0) x10) (λ x13 : ι → ι . setsum (x2 (λ x14 . x13 0) (λ x14 : ι → ι . x0 (λ x15 x16 . λ x17 : ι → ι → ι . λ x18 . 0) 0 (λ x15 : ι → ι . 0)) (λ x14 x15 . 0) (λ x14 x15 . x15) x12) (Inj0 x12))) (setsum 0 0) (λ x9 : ι → ι . x6) = x0 (λ x9 x10 . λ x11 : ι → ι → ι . λ x12 . Inj1 (setsum (Inj1 (x3 (λ x13 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι → ι . 0))) x12)) (setsum (Inj0 0) 0) (λ x9 : ι → ι . setsum (x7 (x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) (setsum 0 0)) (λ x10 . x3 (λ x11 : ι → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . 0) 0))) (setsum x6 x5))) ⟶ False (proof)
Theorem 078d5.. : ∀ x0 : (ι → (ι → ι) → ι) → ι → ι → ι . ∀ x1 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . ∀ x2 : (ι → ι → ι → (ι → ι) → ι) → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → (ι → ι) → ι → ι) → (ι → ι) → ι → ι → ι) → ι → ι . (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 = Inj1 (Inj1 (x4 (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . Inj1 0) (setsum 0 0)) (x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . Inj1 0) x5)))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 = x4) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι) → ι . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x10) 0 = setsum (Inj1 (x6 (λ x9 . 0) (x7 (λ x9 x10 . Inj0 0)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x2 (λ x13 x14 x15 . λ x16 : ι → ι . x1 (λ x17 : ι → ((ι → ι) → ι → ι) → ι . x15) 0) (x1 (λ x13 : ι → ((ι → ι) → ι → ι) → ι . x11) 0)) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . setsum 0 0) (x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . x16) 0)) 0 (Inj1 0)) 0 = setsum 0 0) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x6) (setsum (x2 (λ x9 x10 x11 . λ x12 : ι → ι . x0 (λ x13 . λ x14 : ι → ι . 0) (setsum 0 0) x11) 0) x6) = x6) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 . λ x10 : ι → ι . 0) (Inj1 (x4 (Inj1 0) 0 (setsum (x6 0) (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)) 0)) (x0 (λ x9 . λ x10 : ι → ι . x7) (x4 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7) (setsum 0 0)) (setsum (x6 0) 0) 0 (Inj0 (Inj0 0))) (Inj1 x7)) = setsum 0 0) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι → ι . x0 (λ x9 . λ x10 : ι → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 x15 . x1 (λ x16 : ι → ((ι → ι) → ι → ι) → ι . x15) 0) (x0 (λ x11 . λ x12 : ι → ι . setsum 0 0) (setsum 0 (Inj0 0)) (x0 (λ x11 . λ x12 : ι → ι . 0) (setsum 0 0) 0))) 0 (x0 (λ x9 . λ x10 : ι → ι . setsum (x3 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 x15 . 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . 0) 0)) (x7 (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0)) (λ x11 : ι → ι . 0) (setsum 0 0) (x6 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0)))) (x5 (x0 (λ x9 . λ x10 : ι → ι . x10 0) 0 (x4 0 0 0 0)) (λ x9 x10 . x1 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x3 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0) 0)) 0) = x3 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 x13 . x13) (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x7 0 (λ x9 : ι → ι . 0) (x4 0 0 0 0) (Inj1 0))))) ⟶ False (proof)
Theorem 1ed11.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (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 . (∀ x4 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x3 (λ x9 : (ι → ι → ι) → ι . setsum (x1 (λ x10 x11 . λ x12 : ι → ι . Inj0 x10) (x3 (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 . 0) 0) (λ x10 . λ x11 : ι → ι . x9 (λ x12 x13 . 0)))) (Inj0 (x0 (λ x10 . 0) 0))) (λ x9 . λ x10 : ι → ι . 0) = setsum (Inj0 (Inj0 (setsum x6 (setsum 0 0)))) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι → ι) → ι . x6 (x2 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum (setsum 0 0) (setsum 0 0)) (λ x10 x11 x12 x13 . 0))) (λ x9 . λ x10 : ι → ι . Inj0 0) = x6 (x3 (λ x9 : (ι → ι → ι) → ι . Inj0 0) (λ x9 . λ x10 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 : ((ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x9) (λ x9 x10 x11 x12 . x3 (λ x13 : (ι → ι → ι) → ι . x2 (λ x14 x15 . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0) (λ x14 x15 x16 x17 . x0 (λ x18 . Inj0 0) (Inj1 0))) (λ x13 . λ x14 : ι → ι . x2 (λ x15 x16 . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . Inj0 (Inj0 0)) (λ x15 x16 x17 x18 . x17))) = Inj1 (x3 (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 : (ι → ι → ι) → ι . setsum (x1 (λ x11 x12 . λ x13 : ι → ι . 0) 0) (x0 (λ x11 . 0) 0)) (λ x10 . λ x11 : ι → ι . x11 (x0 (λ x12 . 0) 0))) (λ x9 . λ x10 : ι → ι . x0 (λ x11 . 0) (setsum (x6 (λ x11 x12 : ι → ι . λ x13 . 0) 0) 0)))) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum (x0 (λ x13 . x3 (λ x14 : (ι → ι → ι) → ι . x1 (λ x15 x16 . λ x17 : ι → ι . 0) 0) (λ x14 . λ x15 : ι → ι . x13)) (setsum 0 (setsum 0 0))) (x12 (setsum 0 0))) (λ x9 x10 x11 x12 . Inj0 (setsum (setsum (Inj1 0) x9) 0)) = x4) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 x10 . λ x11 : ι → ι . x1 (λ x12 x13 . λ x14 : ι → ι . 0) x7) x6 = x1 (λ x9 x10 . λ x11 : ι → ι . Inj1 (x1 (λ x12 x13 . λ x14 : ι → ι . setsum (setsum 0 0) (x2 (λ x15 x16 . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . 0) (λ x15 x16 x17 x18 . 0))) x7)) (setsum 0 0)) ⟶ (∀ x4 : (ι → ι) → ι → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι . x10) (x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (λ x9 x10 x11 x12 . Inj0 (setsum x10 (x3 (λ x13 : (ι → ι → ι) → ι . 0) (λ x13 . λ x14 : ι → ι . 0))))) = Inj0 x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → ι . ∀ x7 . x0 (λ x9 . setsum 0 (Inj1 x7)) (x3 (λ x9 : (ι → ι → ι) → ι . x6 (λ x10 : ι → ι → ι . Inj1 (x3 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . 0)))) (λ x9 . λ x10 : ι → ι . setsum (x2 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . Inj0 0) (λ x11 x12 x13 x14 . x3 (λ x15 : (ι → ι → ι) → ι . 0) (λ x15 . λ x16 : ι → ι . 0))) 0)) = Inj0 (setsum 0 (x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (λ x9 x10 x11 x12 . x9)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x0 (λ x9 . x3 (λ x10 : (ι → ι → ι) → ι . setsum 0 0) (λ x10 . λ x11 : ι → ι . setsum x9 0)) (x3 (λ x9 : (ι → ι → ι) → ι . setsum 0 (x5 (λ x10 . λ x11 : ι → ι . λ x12 . 0))) (λ x9 . λ x10 : ι → ι . x3 (λ x11 : (ι → ι → ι) → ι . 0) (λ x11 . λ x12 : ι → ι . x1 (λ x13 x14 . λ x15 : ι → ι . x3 (λ x16 : (ι → ι → ι) → ι . 0) (λ x16 . λ x17 : ι → ι . 0)) (setsum 0 0)))) = setsum (Inj1 (x2 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (λ x9 x10 x11 x12 . x3 (λ x13 : (ι → ι → ι) → ι . x10) (λ x13 . λ x14 : ι → ι . x2 (λ x15 x16 . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . 0) (λ x15 x16 x17 x18 . 0))))) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . Inj0 (x3 (λ x12 : (ι → ι → ι) → ι . x1 (λ x13 x14 . λ x15 : ι → ι . 0) 0) (λ x12 . λ x13 : ι → ι . x3 (λ x14 : (ι → ι → ι) → ι . 0) (λ x14 . λ x15 : ι → ι . 0)))))) ⟶ False (proof)
Theorem 11c22.. : ∀ x0 : ((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 → ι → ι → ι) → ι . ∀ x3 : ((ι → ι → (ι → ι) → ι → ι) → ι) → ((ι → (ι → ι) → ι → ι) → ι → ι → ι → ι) → ι . (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x1 (λ x10 . x0 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . x11 (x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . λ x13 : ι → ι → ι . 0)) (λ x12 : ι → ι . setsum 0 0) (x2 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι . λ x13 . 0) 0 (λ x12 x13 x14 . 0))) (Inj0 (x7 0))) (λ x10 : ι → ι → ι → ι . λ x11 : ι → ι → ι . 0)) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum (setsum (x3 (λ x13 : ι → ι → (ι → ι) → ι → ι . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . λ x15 : ι → ι → ι . 0)) (λ x13 : ι → (ι → ι) → ι → ι . λ x14 x15 x16 . setsum 0 0)) 0) (x0 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . setsum x12 0) (Inj1 (setsum 0 0)))) = x1 (λ x9 . x5 (λ x10 : ι → ι → ι . λ x11 . x2 (λ x12 : (((ι → ι) → ι → ι) → ι) → ι . λ x13 . 0) x9 (λ x12 x13 x14 . x14))) (λ x9 : ι → ι → ι → ι . λ x10 : ι → ι → ι . setsum 0 (x6 (λ x11 . 0)))) ⟶ (∀ x4 : ι → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . Inj0 (x5 (λ x10 . 0))) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 x12 . x11) = setsum (x6 (λ x9 . λ x10 : ι → ι . x2 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι . λ x12 . Inj0 (x10 0)) (Inj1 (x6 (λ x11 . λ x12 : ι → ι . 0))) (λ x11 x12 x13 . Inj0 (Inj1 0)))) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι . λ x10 . setsum (x9 (λ x11 : (ι → ι) → ι → ι . x10)) (x1 (λ x11 . x10) (λ x11 : ι → ι → ι → ι . λ x12 : ι → ι → ι . setsum 0 (x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . λ x14 : ι → ι → ι . 0))))) 0 (λ x9 x10 x11 . 0) = Inj1 (x2 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι . λ x10 . x0 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x12 : ι → ((ι → ι) → ι) → ι → ι . 0) (x9 (λ x12 : (ι → ι) → ι → ι . 0))) 0) (x6 (λ x9 x10 . x0 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . 0) (Inj0 0)) (λ x9 : ι → ι . λ x10 . setsum 0 x7) (x4 (Inj1 0) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . 0) 0))) (λ x9 x10 x11 . x11))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι . λ x10 . setsum (x2 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι . λ x12 . x11 (λ x13 : (ι → ι) → ι → ι . x13 (λ x14 . 0) 0)) x10 (λ x11 x12 x13 . x3 (λ x14 : ι → ι → (ι → ι) → ι → ι . x2 (λ x15 : (((ι → ι) → ι → ι) → ι) → ι . λ x16 . 0) 0 (λ x15 x16 x17 . 0)) (λ x14 : ι → (ι → ι) → ι → ι . λ x15 x16 x17 . x17))) (x1 (λ x11 . x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . λ x13 : ι → ι → ι . x11)) (λ x11 : ι → ι → ι → ι . λ x12 : ι → ι → ι . setsum (x12 0 0) (x11 0 0 0)))) (x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . Inj0 x6) (setsum 0 (x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . x0 (λ x10 : ι → ((ι → ι) → ι) → ι → ι . 0) 0) (x2 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι . λ x10 . 0) 0 (λ x9 x10 x11 . 0))))) (λ x9 x10 x11 . x10) = Inj1 (setsum 0 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . λ x10 : ι → ι → ι . x7 (x0 (λ x11 : ι → ((ι → ι) → ι) → ι → ι . 0) 0)) = x7 (Inj0 (x7 (x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . λ x10 : ι → ι → ι . x10 0 0))))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . setsum (x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . Inj0 (x2 (λ x11 : (((ι → ι) → ι → ι) → ι) → ι . λ x12 . 0) 0 (λ x11 x12 x13 . 0))) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 x13 . x0 (λ x14 : ι → ((ι → ι) → ι) → ι → ι . setsum 0 0) 0)) x6) (λ x9 : ι → ι → ι → ι . λ x10 : ι → ι → ι . Inj0 0) = x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : (ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 . x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . x3 (λ x10 : ι → ι → (ι → ι) → ι → ι . 0) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 x12 x13 . 0)) (x2 (λ x9 : (((ι → ι) → ι → ι) → ι) → ι . λ x10 . x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . λ x12 : ι → ι → ι . x0 (λ x13 : ι → ((ι → ι) → ι) → ι → ι . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . λ x15 : ι → ι → ι . 0)) (x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . λ x14 : ι → ι → ι . 0)))) 0 (λ x9 x10 x11 . 0)) = setsum (x3 (λ x9 : ι → ι → (ι → ι) → ι → ι . x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . λ x11 : ι → ι → ι . 0)) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 x11 x12 . setsum 0 (x2 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι . λ x14 . 0) (x2 (λ x13 : (((ι → ι) → ι → ι) → ι) → ι . λ x14 . 0) 0 (λ x13 x14 x15 . 0)) (λ x13 x14 x15 . x13)))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 : ι → ((ι → ι) → ι) → ι → ι . 0) 0 = x7) ⟶ False (proof)
Theorem 9d79e.. : ∀ x0 : (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 . ∀ x2 : (((((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι) → ι → ι) → ι → ((ι → ι → ι) → ι → ι → ι) → ι . ∀ x3 : (ι → ι → ι) → ι → ι → ι → ι . (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι → ι → ι . x3 (λ x9 x10 . 0) 0 (x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . 0) (x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . x6) x6 (λ x9 : ι → ι → ι . λ x10 x11 . 0)) (λ x9 : ι → ι → ι . λ x10 x11 . x1 (λ x12 x13 . Inj0 0) (λ x12 . x12) (λ x12 . 0) (λ x12 x13 . 0) (setsum (Inj0 0) (x1 (λ x12 x13 . 0) (λ x12 . 0) (λ x12 . 0) (λ x12 x13 . 0) 0 0)) (x3 (λ x12 x13 . 0) x10 x11 (x2 (λ x12 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 . 0) 0 (λ x12 : ι → ι → ι . λ x13 x14 . 0))))) (x7 (λ x9 . x6) x4 0) = x7 (λ x9 . x7 (λ x10 . x6) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . x12 (λ x14 . x2 (λ x15 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 x17 . 0)) (setsum 0 0)) 0) 0) (Inj0 0) (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x3 (λ x9 x10 . x7 (setsum (Inj1 0) (Inj1 (x1 (λ x11 x12 . 0) (λ x11 . 0) (λ x11 . 0) (λ x11 x12 . 0) 0 0)))) 0 (x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . x9 (λ x11 : (ι → ι) → ι . λ x12 . x1 (λ x13 x14 . setsum 0 0) (λ x13 . 0) (λ x13 . setsum 0 0) (λ x13 x14 . 0) 0 (x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 x15 . 0))) (λ x11 : ι → ι . 0)) (x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . Inj1 (x9 (λ x11 : (ι → ι) → ι . λ x12 . 0) (λ x11 : ι → ι . 0))) 0 (λ x9 : ι → ι → ι . λ x10 x11 . 0)) (λ x9 : ι → ι → ι . λ x10 x11 . x11)) (Inj1 (x3 (λ x9 x10 . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . setsum 0 0) x6) (Inj0 (x7 0)) (x3 (λ x9 x10 . x10) (Inj1 0) x4 (setsum 0 0)) (x3 (λ x9 x10 . x3 (λ x11 x12 . 0) 0 0 0) (setsum 0 0) (x3 (λ x9 x10 . 0) 0 0 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . 0) 0)))) = setsum (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x9) (Inj0 (setsum (Inj0 0) 0))) 0) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . Inj0 0) 0 (λ x9 : ι → ι → ι . λ x10 x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . x12) x7) = setsum x7 (setsum (Inj0 (Inj1 (Inj0 0))) (x3 (λ x9 x10 . Inj0 (x2 (λ x11 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x12 . 0) 0 (λ x11 : ι → ι → ι . λ x12 x13 . 0))) 0 x7 0))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . setsum 0 (x2 (λ x11 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x12 . x12) (x3 (λ x11 x12 . 0) (Inj1 0) (setsum 0 0) x10) (λ x11 : ι → ι → ι . λ x12 x13 . x13))) (x3 (λ x9 x10 . x1 (λ x11 x12 . 0) (λ x11 . x10) (λ x11 . 0) (λ x11 x12 . 0) 0 (setsum 0 0)) (x2 (λ x9 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x10 . x6) (Inj1 x6) (λ x9 : ι → ι → ι . λ x10 x11 . setsum x10 (x3 (λ x12 x13 . 0) 0 0 0))) (setsum 0 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . 0) 0)) x4) (λ x9 : ι → ι → ι . λ x10 x11 . x7 (x3 (λ x12 x13 . setsum 0 0) (x2 (λ x12 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 . x0 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 : (ι → ι) → ι → ι . λ x17 . 0) 0) 0 (λ x12 : ι → ι → ι . λ x13 x14 . x3 (λ x15 x16 . 0) 0 0 0)) (setsum (x7 0) 0) 0)) = x3 (λ x9 x10 . x2 (λ x11 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x12 . Inj1 x10) (Inj0 0) (λ x11 : ι → ι → ι . λ x12 x13 . 0)) (x7 (x7 (x7 x6))) (Inj0 (x7 0)) (x7 (Inj0 (setsum (x1 (λ x9 x10 . 0) (λ x9 . 0) (λ x9 . 0) (λ x9 x10 . 0) 0 0) (x1 (λ x9 x10 . 0) (λ x9 . 0) (λ x9 . 0) (λ x9 x10 . 0) 0 0))))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι . x1 (λ x9 x10 . x6) (λ x9 . Inj1 0) (λ x9 . 0) (λ x9 x10 . x9) (Inj0 0) (setsum (x3 (λ x9 x10 . 0) (x3 (λ x9 x10 . 0) (x7 (λ x9 x10 . 0)) (setsum 0 0) (Inj1 0)) (setsum (setsum 0 0) x4) 0) 0) = setsum 0 x6) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . x6) (λ x9 . x1 (λ x10 x11 . 0) (λ x10 . x1 (λ x11 x12 . Inj1 x9) (λ x11 . setsum (x1 (λ x12 x13 . 0) (λ x12 . 0) (λ x12 . 0) (λ x12 x13 . 0) 0 0) (x2 (λ x12 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x13 . 0) 0 (λ x12 : ι → ι → ι . λ x13 x14 . 0))) (λ x11 . x11) (λ x11 x12 . setsum 0 0) 0 0) (setsum x6) (λ x10 x11 . 0) x6 (Inj1 0)) (λ x9 . x3 (λ x10 x11 . Inj1 x10) 0 (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . x12 (λ x14 . 0) x10) x6) x6) (λ x9 x10 . 0) 0 (Inj0 (x3 (λ x9 x10 . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . 0) 0) (Inj0 (x3 (λ x9 x10 . 0) 0 0 0)) 0 0)) = x3 (λ x9 x10 . Inj0 0) (setsum 0 0) (x7 x4) (x7 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x10 (λ x13 : ι → ι . 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . x11 (λ x15 . x12) x12) (setsum (x0 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . 0) 0) (x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 x15 . 0))) (λ x13 : ι → ι → ι . λ x14 x15 . 0)) 0) 0 = x4 0 (λ x9 : ι → ι . setsum (x2 (λ x10 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 . x10 (λ x12 : (ι → ι) → ι . λ x13 . 0) (λ x12 : ι → ι . x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . 0) 0 (λ x13 : ι → ι → ι . λ x14 x15 . 0))) 0 (λ x10 : ι → ι → ι . λ x11 x12 . 0)) (x1 (λ x10 x11 . 0) (λ x10 . x7) (λ x10 . 0) (λ x10 x11 . 0) (x3 (λ x10 x11 . setsum 0 0) 0 x7 x5) (Inj1 (x2 (λ x10 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x11 . 0) 0 (λ x10 : ι → ι → ι . λ x11 x12 . 0)))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → (ι → ι → ι) → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . x0 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 : (ι → ι) → ι → ι . λ x18 . 0) 0) 0 (λ x13 : ι → ι → ι . λ x14 x15 . 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . x3 (λ x13 x14 . 0) 0 (Inj0 0) (x1 (λ x13 x14 . 0) (λ x13 . setsum 0 0) (λ x13 . x11 (λ x14 . 0) 0) (λ x13 x14 . 0) 0 (x10 (λ x13 : ι → ι . 0)))) 0) = x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . setsum (x2 (λ x13 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x14 . Inj1 (x2 (λ x15 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι) → ι . λ x16 . 0) 0 (λ x15 : ι → ι → ι . λ x16 x17 . 0))) (x1 (λ x13 x14 . x3 (λ x15 x16 . 0) 0 0 0) (λ x13 . Inj0 0) (λ x13 . x12) (λ x13 x14 . Inj0 0) (x10 (λ x13 : ι → ι . 0)) (Inj1 0)) (λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 0)) x9) (Inj1 (Inj1 (x7 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . Inj0 0))))) ⟶ False (proof)
Theorem aeb5f.. : ∀ x0 : ((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 → ι) → ι → ι → ι) → ι → (ι → ι → ι) → ι . ∀ x2 : ((((ι → 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 → ι) → ι) → ι . (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 . x0 (λ x13 : ι → ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11 (λ x14 : ι → ι . λ x15 . 0) 0 (λ x14 . 0) 0)) (Inj1 (Inj1 0)) (λ x11 : ι → ι . 0)) 0) (λ x9 . Inj1 x5) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x3 (λ x11 : (ι → ι) → ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . setsum (x1 (λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 . 0)) (x1 (λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 . 0))) (λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 . setsum 0 0) (x9 (λ x12 . setsum 0 0)) (λ x12 x13 . x11 (λ x14 . x0 (λ x15 : ι → ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) 0) (x11 (λ x14 . 0) 0))) (λ x11 . x11) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x3 (λ x13 : (ι → ι) → ι → ι . x10 0) (λ x13 . x11 (λ x14 . Inj0 0)) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . Inj1 (x11 (λ x15 . 0))))) = x3 (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . x7) (setsum (x0 (λ x10 : ι → ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . Inj1 0) (λ x10 . λ x11 : (ι → ι) → ι . Inj0 0) (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 . 0))) (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0)) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x10 (λ x14 x15 . 0)) x7 (λ x10 x11 . x3 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))))) (λ x9 . Inj0 (x3 (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x0 (λ x13 : ι → ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (λ x10 . Inj1 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x3 (λ x12 : (ι → ι) → ι → ι . setsum 0 0) (λ x12 . x2 (λ x13 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x13 : ι → ι . 0)) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum 0 0)))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x6 (x6 x7))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι) → ι . x3 (λ x9 : (ι → ι) → ι → ι . x1 (λ x10 : ((ι → ι) → ι → ι) → ι . x9 (λ x11 . Inj1 (Inj1 0)) (x3 (λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)) (λ x11 . x9 (λ x12 . 0) 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . Inj0 0))) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 . 0)) (λ x9 . x3 (λ x10 : (ι → ι) → ι → ι . setsum x9 (setsum 0 0)) (λ x10 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) = Inj1 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι) → ι . x2 (λ x9 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x0 (λ x10 : ι → ι → (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x11 (λ x15 . x2 (λ x16 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . Inj1 0) (Inj0 0) (λ x16 : ι → ι . x1 (λ x17 : ((ι → ι) → ι → ι) → ι . 0) (λ x17 : (ι → ι → ι) → ι . λ x18 : ι → ι . λ x19 x20 . 0) 0 (λ x17 x18 . 0))) (x2 (λ x15 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x12) 0 (λ x15 : ι → ι . x3 (λ x16 : (ι → ι) → ι → ι . 0) (λ x16 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0)))) (λ x10 . λ x11 : (ι → ι) → ι . x7 (λ x12 : (ι → ι) → ι → ι . λ x13 . x10) (λ x12 . setsum (setsum 0 0) (setsum 0 0))) 0) (x0 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum x11 (setsum x11 0)) (λ x9 . λ x10 : (ι → ι) → ι . x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . Inj0 (x2 (λ x12 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0))) 0 (λ x11 : ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . setsum 0 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 . setsum 0 0) (x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x12 x13 . x12))) x6) (λ x9 : ι → ι . Inj0 (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . x7 (λ x11 : (ι → ι) → ι → ι . λ x12 . Inj0 0) (λ x11 . x7 (λ x12 : (ι → ι) → ι → ι . λ x13 . 0) (λ x12 . 0))) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . setsum (setsum 0 0) 0) x6 (λ x10 x11 . 0))) = Inj0 x5) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x2 (λ x9 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . Inj1 0) x7 (λ x9 : ι → ι . Inj0 0) = x7) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . x2 (λ x10 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x11 : (ι → ι) → ι → ι . x10 (λ x12 : ι → ι . λ x13 . 0) x7 (λ x12 . x3 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) 0) (λ x11 . Inj1 (x3 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x11 (λ x13 . x13))) 0 (λ x10 : ι → ι . x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . Inj0 x7) (x0 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 : (ι → ι) → ι → ι . 0) (λ x16 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0)) (λ x11 . λ x12 : (ι → ι) → ι . 0) 0) (λ x11 : ι → ι . x11 (x3 (λ x12 : (ι → ι) → ι → ι . 0) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0))))) (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 . x9 (λ x13 x14 . 0)) 0 (λ x9 x10 . x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x12 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x0 (λ x13 : ι → ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) x9) x9 (λ x12 : ι → ι . x2 (λ x13 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0)) (Inj1 0) (λ x13 : ι → ι . 0))) 0 (λ x11 : ι → ι . x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x16) (λ x12 . λ x13 : (ι → ι) → ι . x2 (λ x14 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x15 : (ι → ι) → ι → ι . 0) (λ x15 . 0) (λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0)) (Inj1 0) (λ x14 : ι → ι . x0 (λ x15 : ι → ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) 0)) (x3 (λ x12 : (ι → ι) → ι → ι . x1 (λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 . 0)) (λ x12 . 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x3 (λ x14 : (ι → ι) → ι → ι . 0) (λ x14 . 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0))))) = x2 (λ x9 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . Inj0 (x6 0)) (Inj0 (setsum (x1 (λ x9 : ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 . setsum 0 0) (setsum 0 0) (λ x9 x10 . 0)) (x1 (λ x9 : ((ι → ι) → ι → ι) → ι . setsum 0 0) (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 . x12) (setsum 0 0) (λ x9 x10 . x10)))) (λ x9 : ι → ι . x9 0)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι . λ x11 . setsum (setsum x11 (x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0)) (x3 (λ x12 : (ι → ι) → ι → ι . x3 (λ x13 : (ι → ι) → ι → ι . 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0)) (λ x12 . Inj1 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0)))) (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 x12 . x3 (λ x13 : (ι → ι) → ι → ι . x0 (λ x14 : ι → ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . Inj1 (setsum 0 0)) (λ x14 . λ x15 : (ι → ι) → ι . setsum (x13 (λ x16 . 0) 0) (x2 (λ x16 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x16 : ι → ι . 0))) (x0 (λ x14 : ι → ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : (ι → ι) → ι . x13 (λ x16 . 0) 0) (x13 (λ x14 . 0) 0))) (λ x13 . Inj0 x12) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x12)) (Inj1 (x0 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) (x7 (λ x9 : (ι → ι) → ι . λ x10 x11 . x11)))) (λ x9 x10 . Inj0 (Inj0 (setsum (setsum 0 0) (Inj0 0)))) = x3 (λ x9 : (ι → ι) → ι → ι . setsum (x5 (Inj1 (x3 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0))) (λ x10 : ι → ι . 0)) (Inj1 0)) (λ x9 . setsum 0 (x7 (λ x10 : (ι → ι) → ι . λ x11 x12 . 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum (x7 (λ x11 : (ι → ι) → ι . λ x12 x13 . x0 (λ x14 : ι → ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . Inj0 0) (λ x14 . λ x15 : (ι → ι) → ι . 0) (setsum 0 0))) (Inj1 (x7 (λ x11 : (ι → ι) → ι . λ x12 x13 . Inj0 0))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj0 (x10 (λ x14 . 0) (x12 (x0 (λ x14 : ι → ι → (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : (ι → ι) → ι . 0) 0)))) (λ x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι → ι . x9) (λ x11 . Inj0 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x9)) 0 = x3 (λ x9 : (ι → ι) → ι → ι . x2 (λ x10 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x12 : ((ι → ι) → ι → ι) → ι . Inj1 0) (λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 . 0) (x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x12 x13 . Inj0 0)) (x1 (λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 . x1 (λ x15 : ((ι → ι) → ι → ι) → ι . 0) (λ x15 : (ι → ι → ι) → ι . λ x16 : ι → ι . λ x17 x18 . 0) 0 (λ x15 x16 . 0)) 0 (λ x11 x12 . setsum 0 0)) (λ x11 : ι → ι . x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x16) (λ x12 . λ x13 : (ι → ι) → ι . Inj1 0) (x10 (λ x12 : ι → ι . λ x13 . 0) 0 (λ x12 . 0) 0))) (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι → ι . Inj0 0) (λ x11 . x9 (λ x12 . 0) 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x1 (λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 : (ι → ι → ι) → ι . λ x14 : ι → ι . λ x15 x16 . 0) 0 (λ x13 x14 . 0))) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) x7 (λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x12 (λ x13 : ι → ι . λ x14 . 0) 0 (λ x13 . 0) 0) 0 (λ x12 : ι → ι . x0 (λ x13 : ι → ι → (ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : (ι → ι) → ι . 0) 0))) (λ x10 : ι → ι . Inj1 (Inj1 (x2 (λ x11 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x11 : ι → ι . 0))))) (λ x9 . Inj0 (setsum (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0))) (Inj1 x7))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x1 (λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 : (ι → ι → ι) → ι . λ x12 : ι → ι . λ x13 x14 . 0) (x0 (λ x11 : ι → ι → (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . setsum x15 0) (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 : (ι → ι) → ι → ι . Inj1 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x0 (λ x15 : ι → ι → (ι → ι) → ι . λ x16 : (ι → ι) → ι → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0) (λ x15 . λ x16 : (ι → ι) → ι . 0) 0)) (x3 (λ x11 : (ι → ι) → ι → ι . x0 (λ x12 : ι → ι → (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x11 . x2 (λ x12 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . 0) 0 (λ x12 : ι → ι . 0)) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0))) (λ x11 x12 . x12))) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . Inj1 (x2 (λ x14 : ((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . x3 (λ x15 : (ι → ι) → ι → ι . x3 (λ x16 : (ι → ι) → ι → ι . 0) (λ x16 . 0) (λ x16 : (ι → ι) → ι . λ x17 : ι → ι . 0)) (λ x15 . setsum 0 0) (λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0)) x11 (λ x14 : ι → ι . 0))) (λ x9 . λ x10 : (ι → ι) → ι . 0) 0 = x5 (x0 (λ x9 : ι → ι → (ι → ι) → ι . λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : (ι → ι) → ι . setsum (x10 (λ x11 . x9)) 0) (setsum (x3 (λ x9 : (ι → ι) → ι → ι . x6 0 (λ x10 . 0) 0 0) (λ x9 . x1 (λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x10 x11 . 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0)) (Inj1 (x3 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0)))))) ⟶ False (proof)
Theorem c1b22.. : ∀ x0 : (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 . ∀ x3 : (((ι → ι) → ((ι → ι) → ι → ι) → ι → ι) → ι) → ι → ι . (∀ x4 : ((ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0 = x6 (setsum (setsum (setsum x5 0) 0) (Inj0 (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) 0))) (λ x9 : ι → ι . Inj0 (x9 0))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x0 (λ x10 . Inj0 x6) (x5 (λ x10 . x3 (λ x11 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x0 (λ x12 . 0) 0 (λ x12 : ι → ι . 0) (λ x12 : ι → ι . λ x13 . 0) 0 0) (x9 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) 0))) (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . x9 (λ x12 . Inj1 0) (λ x12 : ι → ι . λ x13 . x1 (λ x14 : ι → ι . λ x15 x16 . x14 0) (Inj1 0) (λ x14 x15 : ι → ι . λ x16 . 0) (setsum 0 0)) (Inj0 (setsum 0 0))) x6 (Inj1 (x9 (λ x10 . x2 (λ x11 x12 x13 x14 . 0) 0 (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → ι . λ x11 . x3 (λ x12 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) 0))) 0 = x0 (λ x9 . Inj0 (x1 (λ x10 : ι → ι . λ x11 x12 . 0) (x2 (λ x10 x11 x12 x13 . x11) 0 (λ x10 : ι → ι → ι . x2 (λ x11 x12 x13 x14 . 0) 0 (λ x11 : ι → ι → ι . 0))) (λ x10 x11 : ι → ι . λ x12 . 0) (Inj1 (setsum 0 0)))) x4 (λ x9 : ι → ι . setsum 0 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 : ι → ι . λ x12 x13 . x1 (λ x14 : ι → ι . λ x15 x16 . x16) (Inj0 0) (λ x14 x15 : ι → ι . λ x16 . setsum x16 0) (setsum (x11 0) (x3 (λ x14 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0))) (x2 (λ x11 x12 x13 x14 . x0 (λ x15 . x15) 0 (λ x15 : ι → ι . Inj1 0) (λ x15 : ι → ι . λ x16 . x16) x14 (x3 (λ x15 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0)) (setsum x10 (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0)) (λ x11 : ι → ι → ι . 0)) (λ x11 x12 : ι → ι . x12) (Inj1 (x9 0))) (Inj1 (x0 (λ x9 . setsum (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) (x2 (λ x10 x11 x12 x13 . 0) 0 (λ x10 : ι → ι → ι . 0))) (x0 (λ x9 . Inj1 0) 0 (λ x9 : ι → ι . x7) (λ x9 : ι → ι . λ x10 . 0) (setsum 0 0) (x5 (λ x9 . 0))) (λ x9 : ι → ι . Inj1 (Inj0 0)) (λ x9 : ι → ι . λ x10 . 0) (Inj0 x4) 0)) (x1 (λ x9 : ι → ι . λ x10 x11 . x7) 0 (λ x9 x10 : ι → ι . λ x11 . 0) (x5 (λ x9 . x1 (λ x10 : ι → ι . λ x11 x12 . x0 (λ x13 . 0) 0 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) 0 0) 0 (λ x10 x11 : ι → ι . λ x12 . Inj1 0) (Inj0 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 x10 x11 x12 . 0) (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x5) x5) (λ x9 : ι → ι → ι . Inj1 (x2 (λ x10 x11 x12 x13 . Inj1 x12) (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x6 (λ x11 . 0) 0 (λ x11 . 0)) (setsum 0 0)) (λ x10 : ι → ι → ι . 0))) = Inj0 0) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → (ι → ι) → ι . x2 (λ x9 x10 x11 x12 . 0) (setsum (setsum (x2 (λ x9 x10 x11 x12 . x3 (λ x13 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) 0 (λ x9 : ι → ι → ι . 0)) (x0 (λ x9 . 0) (Inj1 0) (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . setsum 0 0) (setsum 0 0) (x0 (λ x9 . 0) 0 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) 0 0))) (x1 (λ x9 : ι → ι . λ x10 x11 . Inj1 (x7 0 0 (λ x12 . 0))) (x0 (λ x9 . x9) x4 (λ x9 : ι → ι . setsum 0 0) (λ x9 : ι → ι . λ x10 . Inj0 0) (Inj1 0) x4) (λ x9 x10 : ι → ι . λ x11 . 0) x4)) (λ x9 : ι → ι → ι . 0) = setsum (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) (x0 (λ x9 . x7 (setsum 0 0) (setsum 0 0) (λ x10 . setsum 0 0)) x5 (λ x9 : ι → ι . x5) (λ x9 : ι → ι . λ x10 . 0) (x1 (λ x9 : ι → ι . λ x10 x11 . setsum 0 0) (Inj1 0) (λ x9 x10 : ι → ι . λ x11 . Inj1 0) 0) (Inj1 x6))) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ι . λ x10 x11 . x10) x7 (λ x9 x10 : ι → ι . λ x11 . setsum 0 0) 0 = x7) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι) → ι → ι . x1 (λ x9 : ι → ι . λ x10 x11 . x1 (λ x12 : ι → ι . λ x13 x14 . 0) 0 (λ x12 x13 : ι → ι . λ x14 . setsum (setsum x11 (x2 (λ x15 x16 x17 x18 . 0) 0 (λ x15 : ι → ι → ι . 0))) (x3 (λ x15 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) (x1 (λ x15 : ι → ι . λ x16 x17 . 0) 0 (λ x15 x16 : ι → ι . λ x17 . 0) 0))) x11) (x0 (setsum 0) (x2 (λ x9 x10 x11 x12 . x12) (x1 (λ x9 : ι → ι . λ x10 x11 . Inj0 0) (x2 (λ x9 x10 x11 x12 . 0) 0 (λ x9 : ι → ι → ι . 0)) (λ x9 x10 : ι → ι . λ x11 . 0) 0) (λ x9 : ι → ι → ι . x9 x6 (x1 (λ x10 : ι → ι . λ x11 x12 . 0) 0 (λ x10 x11 : ι → ι . λ x12 . 0) 0))) (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . x0 (λ x11 . setsum (x2 (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0)) 0) (x0 (λ x11 . 0) 0 (λ x11 : ι → ι . Inj0 0) (λ x11 : ι → ι . λ x12 . 0) (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (x9 0)) (λ x11 : ι → ι . x2 (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι → ι . Inj1 0)) (λ x11 : ι → ι . λ x12 . 0) 0 (x3 (λ x11 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x11 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0) (x3 (λ x11 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0))) (setsum (Inj0 (x5 0 0)) (x0 (λ x9 . x5 0 0) (Inj1 0) (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . setsum 0 0) (x5 0 0) (x5 0 0))) (x5 (Inj1 (x4 (λ x9 : (ι → ι) → ι . 0))) (x4 (λ x9 : (ι → ι) → ι . 0)))) (λ x9 x10 : ι → ι . λ x11 . x9 0) (Inj0 (x0 (λ x9 . Inj1 (x0 (λ x10 . 0) 0 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . 0) 0 0)) (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x1 (λ x10 : ι → ι . λ x11 x12 . 0) 0 (λ x10 x11 : ι → ι . λ x12 . 0) 0) (x1 (λ x9 : ι → ι . λ x10 x11 . 0) 0 (λ x9 x10 : ι → ι . λ x11 . 0) 0)) (λ x9 : ι → ι . Inj1 (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0)) (λ x9 : ι → ι . λ x10 . setsum (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (x9 0)) (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x6) x6) (x4 (λ x9 : (ι → ι) → ι . x5 0 0)))) = x0 (λ x9 . setsum x9 0) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . x11) (λ x9 : ι → ι . 0) (x5 0 (setsum (x2 (λ x9 x10 x11 x12 . 0) 0 (λ x9 : ι → ι → ι . 0)) (setsum 0 0)))) (λ x9 : ι → ι . x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x0 (λ x11 . 0) (x2 (λ x11 x12 x13 x14 . Inj1 0) (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0) (λ x11 : ι → ι → ι . x10 (λ x12 . 0) (λ x12 : ι → ι . λ x13 . 0) 0)) (λ x11 : ι → ι . x0 (λ x12 . x0 (λ x13 . 0) 0 (λ x13 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . 0) 0 0) (x2 (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0)) (λ x12 : ι → ι . x10 (λ x13 . 0) (λ x13 : ι → ι . λ x14 . 0) 0) (λ x12 : ι → ι . λ x13 . Inj0 0) (Inj1 0) (setsum 0 0)) (λ x11 : ι → ι . λ x12 . 0) (x10 (λ x11 . x7 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 : ι → ι . 0) 0) (λ x11 : ι → ι . λ x12 . 0) (Inj1 0)) (setsum 0 (Inj0 0))) (x1 (λ x10 : ι → ι . λ x11 x12 . x9 (Inj0 0)) (x2 (λ x10 x11 x12 x13 . x12) (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) (λ x10 : ι → ι → ι . x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0) 0)) (λ x10 x11 : ι → ι . λ x12 . setsum (x9 0) (setsum 0 0)) (Inj0 (x5 0 0)))) (λ x9 : ι → ι . λ x10 . setsum (x9 (x0 (λ x11 . x11) (x3 (λ x11 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) (λ x11 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . x1 (λ x13 : ι → ι . λ x14 x15 . 0) 0 (λ x13 x14 : ι → ι . λ x15 . 0) 0) (x2 (λ x11 x12 x13 x14 . 0) 0 (λ x11 : ι → ι → ι . 0)) (x9 0))) 0) (x7 (λ x9 . λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x9 : ι → ι . setsum 0 (x2 (λ x10 x11 x12 x13 . Inj0 0) 0 (λ x10 : ι → ι → ι . x7 (λ x11 . λ x12 : ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0) 0))) (x1 (λ x9 : ι → ι . λ x10 x11 . x0 (λ x12 . x9 0) (x9 0) (λ x12 : ι → ι . x9 0) (λ x12 : ι → ι . λ x13 . setsum 0 0) (x2 (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0)) 0) (setsum (x4 (λ x9 : (ι → ι) → ι . 0)) 0) (λ x9 x10 : ι → ι . λ x11 . Inj1 0) (x0 (λ x9 . 0) (x4 (λ x9 : (ι → ι) → ι . 0)) (λ x9 : ι → ι . x5 0 0) (λ x9 : ι → ι . λ x10 . x9 0) (setsum 0 0) x6))) (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x0 (λ x11 . 0) 0 (λ x11 : ι → ι . 0) (λ x11 : ι → ι . λ x12 . 0) 0 0) (x5 0 0)) x6) (x4 (λ x9 : (ι → ι) → ι . setsum 0 (x9 (λ x10 . 0)))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι) → ι → (ι → ι) → ι → ι . x0 (λ x9 . x7 (λ x10 : (ι → ι) → ι → ι . x1 (λ x11 : ι → ι . λ x12 x13 . x10 (λ x14 . x13) 0) (x7 (λ x11 : (ι → ι) → ι → ι . x7 (λ x12 : (ι → ι) → ι → ι . 0) 0 (λ x12 . 0) 0) 0 (λ x11 . setsum 0 0) (setsum 0 0)) (λ x11 x12 : ι → ι . λ x13 . x10 (λ x14 . setsum 0 0) (x12 0)) (setsum (x2 (λ x11 x12 x13 x14 . 0) 0 (λ x11 : ι → ι → ι . 0)) (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0))) 0 (λ x10 . 0) (setsum (x6 x9) 0)) (Inj0 (setsum (x2 (λ x9 x10 x11 x12 . x11) 0 (λ x9 : ι → ι → ι . 0)) (x6 (Inj1 0)))) (λ x9 : ι → ι . setsum (x7 (λ x10 : (ι → ι) → ι → ι . 0) (x1 (λ x10 : ι → ι . λ x11 x12 . setsum 0 0) 0 (λ x10 x11 : ι → ι . λ x12 . setsum 0 0) (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0)) (λ x10 . x3 (λ x11 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x10) (x1 (λ x11 : ι → ι . λ x12 x13 . 0) 0 (λ x11 x12 : ι → ι . λ x13 . 0) 0)) 0) x5) (λ x9 : ι → ι . λ x10 . 0) (x0 (λ x9 . x1 (λ x10 : ι → ι . λ x11 x12 . x3 (λ x13 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x3 (λ x14 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0) x9) (setsum x5 (x3 (λ x10 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0)) (λ x10 x11 : ι → ι . λ x12 . x0 (λ x13 . Inj0 0) (setsum 0 0) (λ x13 : ι → ι . 0) (λ x13 : ι → ι . λ x14 . x1 (λ x15 : ι → ι . λ x16 x17 . 0) 0 (λ x15 x16 : ι → ι . λ x17 . 0) 0) 0 0) x9) x4 (λ x9 : ι → ι . x6 0) (λ x9 : ι → ι . λ x10 . 0) (Inj1 x5) 0) (x1 (λ x9 : ι → ι . λ x10 x11 . Inj0 (x2 (λ x12 x13 x14 x15 . 0) (setsum 0 0) (λ x12 : ι → ι → ι . Inj1 0))) 0 (λ x9 x10 : ι → ι . λ x11 . Inj1 (x7 (λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . 0) 0) (x7 (λ x12 : (ι → ι) → ι → ι . 0) 0 (λ x12 . 0) 0) (λ x12 . x9 0) (setsum 0 0))) 0) = setsum x5 (Inj0 (setsum 0 (x6 (x7 (λ x9 : (ι → ι) → ι → ι . 0) 0 (λ x9 . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . x1 (λ x10 : ι → ι . λ x11 x12 . 0) (x2 (λ x10 x11 x12 x13 . 0) (x5 (Inj1 0)) (λ x10 : ι → ι → ι . x2 (λ x11 x12 x13 x14 . setsum 0 0) 0 (λ x11 : ι → ι → ι . x9))) (λ x10 x11 : ι → ι . λ x12 . setsum (Inj1 x9) (setsum x9 (setsum 0 0))) 0) (x7 (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . setsum (setsum 0 0) (x7 0 0)) (x4 (λ x9 . x5 0))) (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x2 (λ x10 x11 x12 x13 . Inj1 0) (x2 (λ x10 x11 x12 x13 . 0) 0 (λ x10 : ι → ι → ι . 0)) (λ x10 : ι → ι → ι . x9 (λ x11 . 0) (λ x11 : ι → ι . λ x12 . 0) 0)) (x2 (λ x9 x10 x11 x12 . 0) (setsum 0 0) (λ x9 : ι → ι → ι . setsum 0 0)))) (λ x9 : ι → ι . setsum (setsum 0 0) 0) (λ x9 : ι → ι . λ x10 . 0) 0 x6 = x1 (λ x9 : ι → ι . λ x10 x11 . x7 0 (x3 (λ x12 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . x3 (λ x13 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . Inj1 0) (setsum 0 0)) (x2 (λ x12 x13 x14 x15 . x2 (λ x16 x17 x18 x19 . 0) 0 (λ x16 : ι → ι → ι . 0)) (setsum 0 0) (λ x12 : ι → ι → ι . setsum 0 0)))) (Inj1 (Inj1 0)) (λ x9 x10 : ι → ι . λ x11 . setsum (setsum (x10 x11) 0) (x7 (x0 (λ x12 . x12) 0 (λ x12 : ι → ι . x9 0) (λ x12 : ι → ι . λ x13 . x1 (λ x14 : ι → ι . λ x15 x16 . 0) 0 (λ x14 x15 : ι → ι . λ x16 . 0) 0) (setsum 0 0) (x2 (λ x12 x13 x14 x15 . 0) 0 (λ x12 : ι → ι → ι . 0))) (setsum (Inj0 0) 0))) (Inj0 (x7 (x0 (λ x9 . x1 (λ x10 : ι → ι . λ x11 x12 . 0) 0 (λ x10 x11 : ι → ι . λ x12 . 0) 0) x6 (λ x9 : ι → ι . setsum 0 0) (λ x9 : ι → ι . λ x10 . setsum 0 0) (x5 0) (x3 (λ x9 : (ι → ι) → ((ι → ι) → ι → ι) → ι → ι . 0) 0)) 0))) ⟶ False (proof)
Theorem d5be2.. : ∀ x0 : (((((ι → ι) → ι) → ι) → ι → ι) → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → ι) → ι . ∀ x2 : (((ι → ι → ι) → ι) → ι → ((ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x7 : ι → (ι → ι) → ι → ι . x3 (λ x9 . setsum (x1 (λ x10 . 0) (λ x10 . x7 (x2 (λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (λ x11 . x10) (Inj1 0))) (setsum (x1 (λ x10 . setsum 0 0) (λ x10 . x3 (λ x11 . 0) 0)) (setsum 0 (x7 0 (λ x10 . 0) 0)))) (x1 (λ x9 . Inj1 (x1 (λ x10 . x6 (λ x11 : ι → ι → ι . λ x12 . 0) (λ x11 x12 . 0) 0 0) (λ x10 . 0))) (λ x9 . x7 0 (λ x10 . x0 (λ x11 : (((ι → ι) → ι) → ι) → ι → ι . x10) 0) 0)) = x1 (λ x9 . Inj0 (setsum x9 (Inj0 (Inj1 0)))) (λ x9 . x5)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x3 (λ x9 . 0) x7 = setsum 0 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . setsum (x1 (λ x12 . setsum (x0 (λ x13 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0) x10) (λ x12 . x1 (λ x13 . 0) (λ x13 . x0 (λ x14 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0))) (Inj1 (setsum 0 (x2 (λ x12 : (ι → ι → ι) → ι . λ x13 . λ x14 : (ι → ι) → ι . 0) 0)))) (setsum x5 (Inj0 x4)) = x6 (x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . x6 (x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . x11) x5) 0) (x7 (setsum (setsum 0 0) (Inj1 0)))) (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → (ι → ι) → ι . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . 0) (x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . x3 (λ x10 . x10) x5) (setsum x4 (x2 (λ x9 : (ι → ι → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . setsum 0 0) (Inj1 0)))) = x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . Inj1 (setsum x6 0)) (setsum (setsum (x7 (x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0) (λ x9 . x6)) 0) x5)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x9 . x0 (λ x10 : (((ι → ι) → ι) → ι) → ι → ι . x7) (setsum 0 0)) (λ x9 . setsum (x5 (x0 (λ x10 : (((ι → ι) → ι) → ι) → ι → ι . x2 (λ x11 : (ι → ι → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (setsum 0 0))) (x3 (λ x10 . 0) (x3 (λ x10 . x0 (λ x11 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0) (x3 (λ x10 . 0) 0)))) = x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . Inj1 (Inj0 0)) (x1 (λ x9 . x6 (Inj0 0) (λ x10 : ι → ι . λ x11 . setsum (x0 (λ x12 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0) (x10 0)) 0 0) (λ x9 . Inj0 0))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . x3 (λ x10 . x3 (λ x11 . x0 (λ x12 : (((ι → ι) → ι) → ι) → ι → ι . 0) 0) x6) x6) (setsum 0) = setsum (x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . 0) (setsum (Inj0 (setsum 0 0)) 0)) 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . Inj0 (x5 (setsum (setsum 0 0) (x1 (λ x10 . 0) (λ x10 . 0))) (λ x10 x11 . 0) (λ x10 . Inj0 0))) 0 = Inj0 (Inj1 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → (ι → ι → ι) → (ι → ι) → ι . x0 (λ x9 : (((ι → ι) → ι) → ι) → ι → ι . x9 (λ x10 : (ι → ι) → ι . x9 (λ x11 : (ι → ι) → ι . x7 (x9 (λ x12 : (ι → ι) → ι . 0) 0) (λ x12 x13 . Inj0 0) (λ x12 . x1 (λ x13 . 0) (λ x13 . 0))) 0) 0) (setsum 0 (x3 (λ x9 . 0) (x1 (λ x9 . x7 0 (λ x10 x11 . 0) (λ x10 . 0)) (λ x9 . x1 (λ x10 . 0) (λ x10 . 0))))) = x7 (x3 (λ x9 . 0) (x1 (λ x9 . Inj1 0) (λ x9 . setsum (x7 0 (λ x10 x11 . 0) (λ x10 . 0)) x6))) (λ x9 x10 . Inj0 (setsum (setsum (x1 (λ x11 . 0) (λ x11 . 0)) 0) (x7 x9 (λ x11 x12 . x1 (λ x13 . 0) (λ x13 . 0)) (λ x11 . x10)))) (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . Inj1 (x2 (λ x13 : (ι → ι → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . x15 (λ x16 . 0)) (x12 (λ x13 . 0)))) (x1 (λ x10 . x7 (Inj1 0) (λ x11 x12 . 0) (λ x11 . 0)) (λ x10 . x9)))) ⟶ False (proof)
Theorem 7087a.. : ∀ x0 : (((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) → (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) → ι → ι) → ι → ι) → ι . (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι → ι . ∀ x5 : ((ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : ι → ι . λ x11 x12 . x3 (λ x13 . λ x14 : ι → ι . λ x15 x16 . 0) (λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 . 0)) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . x10) = Inj1 (Inj0 (x4 (λ x9 : (ι → ι) → ι → ι . λ x10 . x10) (x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x2 (λ x14 . 0) (λ x14 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x15 : (ι → ι) → ι . 0)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x3 (λ x9 . λ x10 : ι → ι . λ x11 x12 . setsum (setsum x11 0) 0) (λ x9 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . 0) = x5 (λ x9 : ι → ι → ι . 0)) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 . x0 (λ x10 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . Inj1 (setsum (Inj0 0) (Inj1 0))) (λ x10 : (ι → ι → ι) → ι → ι . Inj1 0)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x1 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι . λ x14 x15 . Inj1 (setsum (x13 0) 0)) (λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 . x10 (λ x14 . 0))) = x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . Inj0 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . Inj1)) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι . x2 (λ x9 . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι . λ x13 x14 . x12 (x3 (λ x15 . λ x16 : ι → ι . λ x17 x18 . 0) (λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 . setsum 0 0))) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . x12)) (λ x9 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x0 (λ x11 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x12 . x12) (λ x12 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . 0)) (λ x11 : (ι → ι → ι) → ι → ι . x11 (λ x12 x13 . 0) (x9 (λ x12 x13 . 0) (λ x12 . 0) (x11 (λ x12 x13 . 0) 0)))) = x0 (λ x9 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . setsum 0 (x7 0 (x2 (λ x10 . x9 (λ x11 . 0) (λ x11 : ι → ι . 0) (λ x11 . 0)) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . 0)))) (λ x9 : (ι → ι → ι) → ι → ι . x7 (x7 (Inj0 (Inj0 0)) (x2 (λ x10 . x7 0 0) (λ x10 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . setsum 0 0))) (Inj0 (Inj1 (x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι . λ x13 x14 . 0) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . 0)))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . 0) = Inj0 (x6 0)) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . x3 (λ x12 . λ x13 : ι → ι . λ x14 x15 . x15) (λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . Inj1 (x0 (λ x14 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . setsum 0 0) (λ x14 : (ι → ι → ι) → ι → ι . 0)))) = setsum (x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x11 (Inj0 (x10 (λ x14 : ι → ι . 0)))) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . 0)) (x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x1 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι . λ x17 x18 . setsum (x2 (λ x19 . 0) (λ x19 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x20 : (ι → ι) → ι . 0)) (x1 (λ x19 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x20 : ((ι → ι) → ι) → ι . λ x21 : ι → ι . λ x22 x23 . 0) (λ x19 . λ x20 : (ι → ι) → ι → ι . λ x21 . 0))) (λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . x13)) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . x0 (λ x12 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . Inj0 x9) (λ x12 : (ι → ι → ι) → ι → ι . 0)))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x1 (λ x10 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι . λ x13 x14 . x12 (x2 (λ x15 . 0) (λ x15 : (ι → ι → ι) → (ι → ι) → ι → ι . λ x16 : (ι → ι) → ι . 0))) (λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 . 0)) (λ x9 : (ι → ι → ι) → ι → ι . setsum (Inj0 (Inj1 x7)) (setsum (setsum (x9 (λ x10 x11 . 0) 0) (setsum 0 0)) 0)) = x1 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι . λ x12 x13 . setsum (x10 (λ x14 : ι → ι . x14 (Inj1 0))) (x1 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι . λ x17 x18 . x1 (λ x19 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x20 : ((ι → ι) → ι) → ι . λ x21 : ι → ι . λ x22 x23 . x23) (λ x19 . λ x20 : (ι → ι) → ι → ι . λ x21 . Inj0 0)) (λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . Inj0 (Inj1 0)))) (λ x9 . λ x10 : (ι → ι) → ι → ι . λ x11 . Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x3 (λ x10 . λ x11 : ι → ι . λ x12 x13 . x1 (λ x14 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x15 : ((ι → ι) → ι) → ι . λ x16 : ι → ι . λ x17 x18 . 0) (λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 . x1 (λ x17 : (((ι → ι) → ι) → ι → ι → ι) → ι . λ x18 : ((ι → ι) → ι) → ι . λ x19 : ι → ι . λ x20 x21 . x21) (λ x17 . λ x18 : (ι → ι) → ι → ι . λ x19 . x16))) (λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 . x11)) (λ x9 : (ι → ι → ι) → ι → ι . x0 (λ x10 : (ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι . x7) (λ x10 : (ι → ι → ι) → ι → ι . 0)) = Inj1 (x4 (setsum 0 0))) ⟶ False (proof)
Theorem 479b0.. : ∀ x0 : (ι → ι) → (ι → ι) → ((ι → ι → ι) → ι) → ι . ∀ x1 : (ι → (ι → (ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : (ι → ι) → ι . Inj0 x6) (λ x9 . x9) (x0 (λ x9 . x6) (λ x9 . x0 (λ x10 . 0) (λ x10 . Inj1 (setsum 0 0)) (λ x10 : ι → ι → ι . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . x3 (λ x15 : (ι → ι) → ι . 0) (λ x15 . 0) 0) 0)) (λ x9 : ι → ι → ι . x0 (λ x10 . 0) (λ x10 . setsum (Inj1 0) x6) (λ x10 : ι → ι → ι . Inj0 0))) = x0 (λ x9 . x9) (λ x9 . x9) (λ x9 : ι → ι → ι . setsum (x3 (λ x10 : (ι → ι) → ι . x7) (λ x10 . 0) x6) (x9 (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . 0) x5) 0))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 : (ι → ι) → ι . x9 (λ x10 . x10)) (λ x9 . x3 (λ x10 : (ι → ι) → ι . x7 (setsum 0 (x7 0 (λ x11 x12 . 0))) (λ x11 x12 . 0)) (λ x10 . x9) (Inj1 x6)) 0 = setsum x6 x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ((ι → ι → ι) → ι) → ι → ι . x2 (λ x9 . x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . Inj1 (x13 0)) (x7 (λ x10 : ι → ι → ι . setsum (x0 (λ x11 . 0) (λ x11 . 0) (λ x11 : ι → ι → ι . 0)) (x7 (λ x11 : ι → ι → ι . 0) 0)) (Inj1 (Inj1 0)))) (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . setsum (x2 (λ x13 . 0) (x3 (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0) 0)) 0) 0) = Inj0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 . x7) (x0 (λ x9 . x0 (λ x10 . setsum x7 0) (λ x10 . x0 (λ x11 . x1 (λ x12 . λ x13 : ι → (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . 0) 0) (λ x11 . setsum 0 0) (λ x11 : ι → ι → ι . 0)) (λ x10 : ι → ι → ι . Inj1 (Inj1 0))) (λ x9 . x6) (λ x9 : ι → ι → ι . x5 0)) = Inj1 (x2 (λ x9 . setsum x7 (Inj1 (x5 0))) 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x2 (λ x13 . x12 (x3 (λ x14 : (ι → ι) → ι . x3 (λ x15 : (ι → ι) → ι . 0) (λ x15 . 0) 0) (λ x14 . 0) (Inj0 0))) 0) (Inj0 x7) = Inj1 (Inj1 (setsum x7 (x2 (λ x9 . Inj0 0) (x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . 0) 0))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x1 (λ x9 . λ x10 : ι → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . x10 0 (λ x13 . 0)) 0 = x5) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → (ι → ι) → ι) → ι → ι → ι . x0 (λ x9 . 0) (λ x9 . x0 (λ x10 . x6 (λ x11 . 0) (λ x11 . 0) (λ x11 . setsum (x3 (λ x12 : (ι → ι) → ι . 0) (λ x12 . 0) 0) (setsum 0 0)) (x2 (λ x11 . x9) (x3 (λ x11 : (ι → ι) → ι . 0) (λ x11 . 0) 0))) (x6 (λ x10 . x10) (λ x10 . Inj0 0) (λ x10 . x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) (x1 (λ x11 . λ x12 : ι → (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . 0) 0))) (λ x10 : ι → ι → ι . 0)) (λ x9 : ι → ι → ι . 0) = Inj1 (x3 (λ x9 : (ι → ι) → ι . x5 (setsum 0 (x6 (λ x10 . 0) (λ x10 . 0) (λ x10 . 0) 0))) (λ x9 . x7 (λ x10 . λ x11 : ι → ι . Inj1 x9) (x1 (λ x10 . λ x11 : ι → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . Inj1 0) (Inj1 0)) 0) (setsum (Inj0 (x7 (λ x9 . λ x10 : ι → ι . 0) 0 0)) (Inj1 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → (ι → ι) → ι → ι → ι . ∀ x7 . x0 (λ x9 . x3 (λ x10 : (ι → ι) → ι . setsum (x10 (λ x11 . 0)) (x3 (λ x11 : (ι → ι) → ι . x10 (λ x12 . 0)) (λ x11 . x3 (λ x12 : (ι → ι) → ι . 0) (λ x12 . 0) 0) 0)) (λ x10 . 0) (setsum (x3 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) (Inj1 0)) (Inj1 0))) (λ x9 . x2 (λ x10 . x2 (setsum (setsum 0 0)) 0) (setsum x7 0)) (λ x9 : ι → ι → ι . x5 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x1 (λ x13 . λ x14 : ι → (ι → ι) → ι . λ x15 : ι → ι → ι . λ x16 : ι → ι . Inj1 0) (Inj1 0))) = setsum 0 (x2 (λ x9 . 0) 0)) ⟶ False (proof)
Theorem ea880.. : ∀ x0 : (ι → (((ι → ι) → ι) → ι) → ι → ι → ι) → ι → ι → ι → ι → ι → ι . ∀ x1 : ((ι → ι) → ι) → ι → ι . ∀ x2 : (ι → ι → ι) → ι → ι . ∀ x3 : ((ι → ι) → ι → ((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ((ι → ι) → ι) → ι) → (ι → ι) → ι . (∀ x4 : ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . x2 (λ x15 x16 . x15) 0) (setsum (x10 (λ x11 . 0)) (x2 (λ x11 x12 . 0) (setsum 0 0))) (setsum (Inj1 x6) x9) (setsum (setsum (x0 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . 0) 0 0 0 0 0) (Inj0 0)) 0) (x10 (λ x11 . x2 (λ x12 x13 . Inj0 0) 0)) 0) (λ x9 . x6) = x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . setsum (x2 (λ x13 x14 . setsum (setsum 0 0) (x0 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 x18 . 0) 0 0 0 0 0)) (Inj1 x11)) (Inj0 (Inj1 (x2 (λ x13 x14 . 0) 0)))) (setsum (Inj1 0) (x1 (λ x9 : ι → ι . setsum x6 (setsum 0 0)) 0)) (setsum (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 (Inj1 (x1 (λ x9 : ι → ι . 0) 0)) (setsum (x4 0) 0) (x7 (λ x9 x10 : ι → ι . Inj1 0) (λ x9 x10 . Inj0 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . Inj0 0) (x4 0) (x2 (λ x9 x10 . 0) 0) (Inj1 0) (x7 (λ x9 x10 : ι → ι . 0) (λ x9 x10 . 0)) x6)) (x5 (λ x9 . Inj1 0))) (x5 (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x2 (λ x14 x15 . Inj1 0) (x2 (λ x14 x15 . 0) 0)) (setsum (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0 0 0 0 0) x6) (setsum (x3 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x10 . 0)) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0 0 0 0 0)) x6 0 0)) (setsum (x7 (λ x9 x10 : ι → ι . Inj1 (setsum 0 0)) (λ x9 x10 . setsum (x2 (λ x11 x12 . 0) 0) 0)) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) (x1 (λ x9 : ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0 0 0 0 0) 0) (x2 (λ x9 x10 . Inj1 0) (setsum 0 0)) 0 0 0)) (x2 (λ x9 x10 . x9) (x4 (setsum 0 (x2 (λ x9 x10 . 0) 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x2 (λ x13 x14 . 0) (x11 (λ x13 . x10) 0)) (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 . Inj0 (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) (setsum (setsum 0 0) x5) 0 (Inj0 (Inj1 0)) (x2 (λ x10 x11 . 0) (x6 0)) (x2 (λ x10 x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . 0) 0 0 0 0 0) x5))) = Inj0 (x6 (x7 (λ x9 . x7 (λ x10 . x10))))) ⟶ (∀ x4 x5 . ∀ x6 x7 : ι → ι . x2 (λ x9 . Inj0) 0 = x5) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι → ι . ∀ x7 . x2 (λ x9 x10 . x10) x7 = x7) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x9 : ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) (setsum (Inj0 (x1 (λ x10 : ι → ι . 0) 0)) (x1 (λ x10 : ι → ι . 0) (x1 (λ x10 : ι → ι . 0) 0))) 0 (setsum (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . x0 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 x17 . 0) 0 0 0 0 0) (x5 0 (λ x10 : ι → ι . 0) 0 0) (x3 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x10 . 0)) 0 0 (setsum 0 0)) (x9 0)) (x2 (λ x10 x11 . 0) (Inj0 x6)) 0) 0 = x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x9) (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . setsum (x1 (λ x13 : ι → ι . setsum 0 0) (x9 0)) (x0 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . x3 (λ x17 : ι → ι . λ x18 . λ x19 : (ι → ι) → ι → ι . λ x20 : ι → ι . 0) (λ x17 . λ x18 : (ι → ι) → ι . 0) (λ x17 . 0)) (x9 0) (x1 (λ x13 : ι → ι . 0) 0) (x11 (λ x13 . 0) 0) 0 (x0 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . 0) 0 0 0 0 0))) (λ x9 . λ x10 : (ι → ι) → ι . setsum (Inj1 x6) (Inj1 0)) (λ x9 . setsum (x5 0 (λ x10 : ι → ι . Inj0 0) 0 (setsum 0 0)) (Inj1 (x7 (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . 0))))) (Inj1 (setsum (setsum (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 0 0 0 0) (x5 0 (λ x9 : ι → ι . 0) 0 0)) (Inj1 (x2 (λ x9 x10 . 0) 0)))) (x2 (λ x9 x10 . x10) (x5 (setsum (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 . 0)) (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0))) (λ x9 : ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0 x6 x6 (x3 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x10 . 0)) (x5 0 (λ x10 : ι → ι . 0) 0 0)) 0 (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . setsum 0 0) (λ x9 . λ x10 : (ι → ι) → ι . Inj0 0) (λ x9 . x1 (λ x10 : ι → ι . 0) 0)))) (setsum (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) (Inj0 (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 . 0))) (Inj0 (x2 (λ x9 x10 . 0) 0)) (Inj0 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0))) (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x2 (λ x13 x14 . 0) 0) (λ x9 . λ x10 : (ι → ι) → ι . x2 (λ x11 x12 . 0) 0) (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) 0 0 0 0 0)) (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . x10 0))) (x5 0 (λ x9 : ι → ι . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 (setsum 0 0) (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . 0)) (setsum 0 0)) 0)) (setsum (x2 (λ x9 x10 . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 0 (Inj0 0) (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . 0) (λ x9 . λ x10 : (ι → ι) → ι . 0) (λ x9 . 0)) x4)) (setsum 0 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x1 (λ x9 : ι → ι . x1 (λ x10 : ι → ι . setsum (Inj0 (x7 0 0)) (setsum (x3 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . 0) (λ x11 . λ x12 : (ι → ι) → ι . 0) (λ x11 . 0)) 0)) (x7 (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) (x3 (λ x10 : ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . 0) (λ x10 . λ x11 : (ι → ι) → ι . 0) (λ x10 . 0)) (x7 0 0) 0 (Inj1 0) 0) (x2 (λ x10 x11 . x1 (λ x12 : ι → ι . 0) 0) (x7 0 0)))) x5 = setsum x6 (Inj1 (x4 x5))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x11) (x1 (λ x9 : ι → ι . 0) (setsum x5 (x3 (λ x9 : ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x9 0) (λ x9 . λ x10 : (ι → ι) → ι . x10 (λ x11 . 0)) (λ x9 . Inj0 0)))) (x6 (λ x9 . 0) 0) (x4 (setsum 0 (setsum (x6 (λ x9 . 0) 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 0 0 0 0))) (λ x9 : ι → ι . λ x10 . x7 (setsum 0 (x6 (λ x11 . 0) 0))) (Inj0 (x2 (λ x9 x10 . setsum 0 0) (x2 (λ x9 x10 . 0) 0)))) (x6 (λ x9 . 0) (x6 (λ x9 . 0) (Inj1 (setsum 0 0)))) (x1 (λ x9 : ι → ι . Inj1 (setsum 0 (x6 (λ x10 . 0) 0))) (x2 (λ x9 x10 . 0) 0)) = x6 (λ x9 . x5) (Inj1 (x6 (λ x9 . x9) (Inj1 0)))) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x1 (λ x13 : ι → ι . Inj1 (x10 (λ x14 : ι → ι . x2 (λ x15 x16 . 0) 0))) (x3 (λ x13 : ι → ι . λ x14 . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . x15 (λ x17 . x14) (Inj1 0)) (λ x13 . λ x14 : (ι → ι) → ι . 0) (λ x13 . setsum x13 (x3 (λ x14 : ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . 0) (λ x14 . λ x15 : (ι → ι) → ι . 0) (λ x14 . 0))))) 0 x5 (x7 (λ x9 x10 . x1 (λ x11 : ι → ι . Inj0 0) x6) (λ x9 : ι → ι . λ x10 . x3 (λ x11 : ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . x12) (λ x11 . λ x12 : (ι → ι) → ι . x0 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . x14 (λ x17 : ι → ι . 0)) x10 (Inj1 0) (setsum 0 0) (setsum 0 0) 0) (λ x11 . Inj1 (x9 0))) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . x1 (λ x13 : ι → ι . 0) (Inj1 0)) (Inj1 0) 0 x6 0 (Inj1 0)) (setsum x5 0)) (x7 (λ x9 x10 . 0) (λ x9 : ι → ι . λ x10 . x9 0) 0 (x7 (λ x9 x10 . x7 (λ x11 x12 . 0) (λ x11 : ι → ι . λ x12 . setsum 0 0) (Inj1 0) 0) (λ x9 : ι → ι . λ x10 . x9 (Inj0 0)) 0 (Inj1 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) 0 0 0 0 0)))) x5 = Inj0 (x1 (λ x9 : ι → ι . 0) 0)) ⟶ False (proof)
Theorem 5d624.. : ∀ x0 : (ι → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : (ι → ι → ι) → ι → ι . ∀ x2 : (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 . (∀ x4 : (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x6) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . setsum 0 0) x7 (x1 (λ x9 x10 . x10) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) x7 0 (λ x9 : ι → ι . λ x10 . x6) 0 x7)) (λ x9 : ι → ι . λ x10 . 0) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x5) (x4 (λ x9 : (ι → ι) → ι . setsum 0 0) (x2 (λ x9 . 0) 0 (λ x9 . 0) (λ x9 . 0)) x7) (x2 (λ x9 . x6) 0 (λ x9 . Inj0 0) (λ x9 . setsum 0 0)) (λ x9 : ι → ι . λ x10 . x6) (Inj0 0) (x4 (λ x9 : (ι → ι) → ι . setsum 0 0) (Inj0 0) (x0 (λ x9 . 0) (λ x9 : (ι → ι) → ι . 0)))) (x4 (λ x9 : (ι → ι) → ι . 0) (x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) (λ x9 : (ι → ι) → ι . Inj0 0)) x6)) (x2 (λ x9 . 0) (setsum (setsum x5 (setsum 0 0)) (x2 (λ x9 . x5) (Inj0 0) (λ x9 . x7) (λ x9 . x2 (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0)))) (λ x9 . x0 (λ x10 . x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) (Inj0 0) (x2 (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0)) (λ x11 : ι → ι . λ x12 . x10) (x1 (λ x11 x12 . 0) 0) (setsum 0 0)) (λ x10 : (ι → ι) → ι . x10 (λ x11 . x2 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0)))) (λ x9 . x7)) (λ x9 : ι → ι . λ x10 . x2 (λ x11 . x11) (setsum (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . Inj1 0) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) (x2 (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0)) (λ x11 : ι → ι . λ x12 . Inj0 0) x10 (x9 0)) (setsum (x9 0) (Inj1 0))) (λ x11 . Inj0 (Inj1 (Inj0 0))) (λ x11 . Inj1 (setsum (Inj1 0) 0))) (x2 (setsum (setsum 0 (x0 (λ x9 . 0) (λ x9 : (ι → ι) → ι . 0)))) (Inj0 0) (λ x9 . x0 (λ x10 . setsum (x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)) 0) (λ x10 : (ι → ι) → ι . 0)) (λ x9 . 0)) (x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)) (x0 (λ x10 . x2 (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0)) (λ x10 : (ι → ι) → ι . x2 (λ x11 . 0) 0 (λ x11 . 0) (λ x11 . 0))) (Inj1 x7) (λ x10 : ι → ι . λ x11 . x0 (λ x12 . 0) (λ x12 : (ι → ι) → ι . x12 (λ x13 . 0))) 0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . setsum (x1 (λ x11 x12 . 0) 0) (x9 (λ x11 . 0))) 0 0 (λ x10 : ι → ι . λ x11 . x10 0) (setsum x6 (Inj1 0)) (x9 (λ x10 . x9 (λ x11 . 0))))) = x0 (λ x9 . setsum x5 (setsum 0 x6)) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x1 (λ x11 x12 . Inj1 (setsum 0 0)) (x2 (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) (x9 (λ x11 . 0)) (λ x11 . x2 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0)) (λ x11 . x10))))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . Inj1 0) 0 0 (λ x9 : ι → ι . λ x10 . 0) 0 (x4 (λ x9 . setsum (Inj1 (x6 0)) x5)) = setsum 0 (x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . x2 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0))) (Inj0 x9) (setsum 0 (setsum 0 0)) (λ x10 : ι → ι . λ x11 . setsum 0 (Inj0 0)) (x1 (λ x10 x11 . x0 (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0)) 0) (Inj1 0)) (λ x9 : (ι → ι) → ι . setsum 0 (Inj0 x5)))) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x7 . x2 (λ x9 . 0) 0 (λ x9 . setsum x7 (x5 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x10 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0)) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) (λ x10 : ι → ι . λ x11 . 0) (Inj1 0) 0))) (λ x9 . Inj1 (x6 (λ x10 . λ x11 : ι → ι . x0 (λ x12 . setsum 0 0) (λ x12 : (ι → ι) → ι . x11 0)) (λ x10 : ι → ι . setsum (x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)) (x10 0)))) = x4 0) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ((ι → ι) → ι) → (ι → ι) → ι . x2 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x7 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x2 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0)) 0 (setsum 0 0) (λ x11 : ι → ι . λ x12 . 0) x6 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) 0 0)) (λ x11 : ι → ι . 0) (λ x11 . Inj1 (Inj0 0))) (x5 (λ x10 . x9) (x2 (λ x10 . Inj0 0) 0 (λ x10 . x10) (λ x10 . x7 0 (λ x11 : ι → ι . 0) (λ x11 . 0))) (λ x10 . x0 (λ x11 . x10) (λ x11 : (ι → ι) → ι . x7 0 (λ x12 : ι → ι . 0) (λ x12 . 0)))) (x2 (λ x10 . setsum (Inj1 0) (setsum 0 0)) (setsum (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) (Inj0 0)) (λ x10 . x10) (λ x10 . x10)) (λ x10 : ι → ι . λ x11 . Inj0 (setsum (x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) (Inj1 0))) 0 (x7 x9 (λ x10 : ι → ι . 0) (λ x10 . x10))) (setsum (x0 (λ x9 . x2 (λ x10 . 0) x9 (λ x10 . x6) (λ x10 . x6)) (λ x9 : (ι → ι) → ι . setsum (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) 0)) 0) (λ x9 . 0) (λ x9 . 0) = Inj0 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x1 (λ x9 x10 . 0) (x1 (λ x9 x10 . 0) (x1 (λ x9 x10 . x6) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x6) 0 0 (λ x9 : ι → ι . λ x10 . Inj1 0) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0) 0 0) (x7 0 0 (λ x9 . 0) 0)))) = x1 (λ x9 x10 . x10) (x7 (x0 (λ x9 . x6) (λ x9 : (ι → ι) → ι . Inj1 (x2 (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0)))) (x2 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . Inj0 0) x6 0 (λ x10 : ι → ι . λ x11 . x7 0 0 (λ x12 . 0) 0) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) 0) (x2 (λ x9 . Inj0 0) (x5 0) (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) (λ x9 . 0)) (λ x9 . Inj0 (x7 0 0 (λ x10 . 0) 0)) (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x7 0 0 (λ x11 . 0) 0) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) (λ x10 : ι → ι . λ x11 . 0) x6 (setsum 0 0))) (λ x9 . setsum 0 (setsum (x5 0) (x7 0 0 (λ x10 . 0) 0))) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 x10 . x7 (setsum (x6 (λ x11 : (ι → ι) → ι . 0)) 0)) 0 = x7 (Inj0 (Inj1 (setsum (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0) 0 0) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0) 0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . Inj0 0) (x5 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x9) (setsum 0 0) 0 (λ x10 : ι → ι . λ x11 . setsum 0 0) (Inj1 0) (Inj1 0))) 0 (λ x10 : ι → ι . λ x11 . 0) (Inj0 (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)) (setsum 0 0) x6 (λ x10 : ι → ι . λ x11 . x7) 0 x7)) (setsum (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) (x2 (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0)) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) (λ x10 : ι → ι . λ x11 . 0) x7 (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0))) 0)) (λ x9 : (ι → ι) → ι . x9 (λ x10 . x0 (λ x11 . Inj0 0) (λ x11 : (ι → ι) → ι . Inj1 (Inj0 0)))) = x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . setsum 0 x7) (setsum 0 (Inj0 x6)) (x2 (λ x9 . x6) 0 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . setsum 0 x9) (setsum (x5 0) x6) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) 0 (Inj0 0) (λ x10 : ι → ι . λ x11 . x7) (x2 (λ x10 . 0) 0 (λ x10 . 0) (λ x10 . 0)) 0) (λ x10 : ι → ι . λ x11 . Inj0 0) x7 x7) (λ x9 . x5 0)) (λ x9 : ι → ι . λ x10 . Inj0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 x7 (λ x11 : ι → ι . λ x12 . Inj0 0) (x9 (Inj0 0)) x6)) (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x5 x7) 0 (x5 (setsum (setsum 0 0) (Inj1 0))) (λ x9 : ι → ι . λ x10 . x2 (λ x11 . 0) (setsum x6 x10) (λ x11 . x0 (λ x12 . Inj1 0) (λ x12 : (ι → ι) → ι . x12 (λ x13 . 0))) (λ x11 . 0)) (x2 (λ x9 . x7) x7 (λ x9 . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) (Inj0 0) (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) (λ x10 : ι → ι . λ x11 . 0) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)) x6) (λ x9 . x1 (λ x10 x11 . x2 (λ x12 . 0) 0 (λ x12 . 0) (λ x12 . 0)) (x0 (λ x10 . 0) (λ x10 : (ι → ι) → ι . 0)))) (x0 (λ x9 . x6) (λ x9 : (ι → ι) → ι . setsum (x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) 0 0) 0))) (Inj0 (x1 (λ x9 x10 . x0 (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι . 0) 0 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) (λ x11 : (ι → ι) → ι . setsum 0 0)) 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . x5) (λ x9 : (ι → ι) → ι . 0) = setsum x6 0) ⟶ False (proof)
Theorem 7afb6.. : ∀ x0 : (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 . ∀ x5 x6 x7 . x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . 0) (λ x9 . x7) (Inj1 x6) 0 = setsum (x4 (x4 x5)) x7) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . setsum (Inj1 (x1 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 x15 . Inj1 0) x10)) 0) (λ x9 . x9) (x7 (setsum (x4 (x5 (λ x9 . 0)) (x4 0 0 0 0) 0 (x5 (λ x9 . 0))) 0)) (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . x3 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 . Inj0 (setsum 0 0)) (λ x11 . x10) (x7 (x1 (λ x11 : ι → ι . λ x12 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x13 x14 x15 . 0) 0)) x10) (λ x9 . x9) (x0 (λ x9 x10 . λ x11 : ι → ι → ι . x11 0 (x3 (λ x12 : ι → ((ι → ι) → ι) → ι . λ x13 . 0) (λ x12 . 0) 0 0)) (x4 0 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . 0) 0 (λ x9 . 0)) (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . 0) 0) 0) (λ x9 . 0)) (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . x10) (setsum x6 (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . 0) 0)))) = setsum (setsum (setsum 0 (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . setsum 0 0) (λ x9 . x6) (setsum 0 0) (x7 0))) (x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x3 (λ x14 : ι → ((ι → ι) → ι) → ι . λ x15 . x14 0 (λ x16 : ι → ι . 0)) (λ x14 . x1 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x17 x18 x19 . 0) 0) (x3 (λ x14 : ι → ((ι → ι) → ι) → ι . λ x15 . 0) (λ x14 . 0) 0 0) (x0 (λ x14 x15 . λ x16 : ι → ι → ι . 0) 0 (λ x14 . 0))) x6)) x6) ⟶ (∀ x4 : ι → ι . ∀ x5 : ((ι → ι) → ι) → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . Inj1 (x0 (λ x11 x12 . λ x13 : ι → ι → ι . Inj0 x10) (x7 (x2 (λ x11 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x12 . 0) 0)) (λ x11 . x10))) 0 = x7 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι → ι) → ι → (ι → ι) → ι . x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . x6) (Inj1 (Inj0 (Inj1 0))) = x6) ⟶ (∀ x4 : ι → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x11) (setsum (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (Inj0 0) 0) (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . x2 (λ x11 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x12 . 0) 0) (x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) 0))) (x4 0 (λ x9 . setsum (x0 (λ x10 x11 . λ x12 : ι → ι → ι . 0) 0 (λ x10 . 0)) (setsum 0 0)))) = x7) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . x11) 0 = x6) ⟶ (∀ x4 x5 x6 . ∀ x7 : ((ι → ι) → ι) → ι → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . x0 (λ x11 x12 . λ x13 : ι → ι → ι . 0) 0 (λ x11 . 0)) 0) (λ x9 . 0) = x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . setsum (x7 (λ x11 : ι → ι . setsum (setsum 0 0) (x11 0)) x6) (setsum x10 (setsum (x2 (λ x11 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x12 . 0) 0) 0))) x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → ι . x0 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (Inj1 (x6 (λ x9 . λ x10 : ι → ι . λ x11 . x9) (x4 0 0) (setsum (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . 0) 0) 0) (x0 (λ x9 x10 . λ x11 : ι → ι → ι . setsum 0 0) (x4 0 0) (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 . 0) (λ x10 . 0) 0 0)))) (λ x9 . 0) = x6 (λ x9 . λ x10 : ι → ι . λ x11 . Inj1 0) (x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . 0) (λ x9 . Inj0 (x1 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x12 x13 x14 . 0) 0)) 0 (x0 (λ x9 x10 . λ x11 : ι → ι → ι . 0) (x3 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 . 0) (λ x9 . 0) 0 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι → ι . λ x11 . 0))))) 0 (setsum (x6 (λ x9 . λ x10 : ι → ι . λ x11 . x7 (λ x12 : (ι → ι) → ι → ι . λ x13 . x2 (λ x14 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x15 . 0) 0)) (x4 (x2 (λ x9 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . λ x10 . 0) 0) (x1 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → ι → ι → ι . λ x11 x12 x13 . 0) 0)) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ((ι → ι) → ι) → ι . λ x13 . 0) (λ x12 . 0) 0 0)) (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . Inj1 0))) (setsum (setsum 0 (x7 (λ x9 : (ι → ι) → ι → ι . λ x10 . 0))) 0))) ⟶ False (proof)
Theorem 000be.. : ∀ x0 : (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) → ι) → ι → ι → ι . ∀ x3 : (ι → (((ι → ι) → ι) → ι) → ι → ι) → (((ι → ι) → ι → ι) → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 . x10 (λ x12 : ι → ι . 0)) (λ x9 : (ι → ι) → ι → ι . 0) (Inj0 (setsum (x0 (λ x9 x10 x11 . 0) (x4 0)) 0)) = setsum (x7 (λ x9 : ι → ι . Inj1 (x0 (λ x10 x11 x12 . x11) (setsum 0 0))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . Inj0 (setsum 0 0)) (λ x11 : (ι → ι) → ι → ι . 0) (x0 (λ x11 x12 x13 . x11) 0)) (λ x9 . x7 (λ x10 : ι → ι . 0) (λ x10 : ι → ι . λ x11 . Inj0 (Inj0 0)) (λ x10 . x0 (λ x11 x12 x13 . setsum 0 0) 0) 0) (x7 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . x13 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0) 0) (λ x9 . 0) (setsum (x7 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) (setsum 0 0)))) 0) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → (ι → ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ((ι → ι) → ι) → ι . λ x11 . setsum (x2 (λ x12 x13 x14 : ι → ι . λ x15 . x13 0) (λ x12 : (ι → ι → ι) → ι . x10 (λ x13 : ι → ι . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0)) 0 x7) (setsum x9 (Inj1 0))) (λ x9 : (ι → ι) → ι → ι . setsum (Inj0 0) 0) 0 = Inj1 (x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 x15 . x2 (λ x16 x17 x18 : ι → ι . λ x19 . 0) (λ x16 : (ι → ι → ι) → ι . x15) x12 0) (Inj1 0)) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x0 (λ x12 x13 x14 . setsum (x1 (λ x15 x16 . λ x17 : ι → ι . λ x18 . 0) (λ x15 : ι → ι → ι → ι . λ x16 x17 . 0) 0) x12) (x1 (λ x12 x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) (λ x12 : ι → ι → ι → ι . λ x13 x14 . Inj1 0) x10)) (Inj0 (setsum (x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . 0) 0 0) (setsum 0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ((ι → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . x7 (setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0) 0) (x6 (x7 0) (λ x10 . x6 0 (λ x11 . 0))))) (x7 (Inj1 (Inj0 (setsum 0 0)))) (setsum 0 (x5 (λ x9 x10 : ι → ι . Inj1 (x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . 0) 0)) (λ x9 : ι → ι . x9 (x6 0 (λ x10 . 0))))) = x7 (setsum (x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) (x11 0)) (λ x9 : (ι → ι → ι) → ι . x5 (λ x10 x11 : ι → ι . 0) (λ x10 : ι → ι . setsum 0 0)) (x6 0 (λ x9 . 0)) 0) (setsum 0 (x5 (λ x9 x10 : ι → ι . Inj0 0) (λ x9 : ι → ι . Inj1 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (Inj1 (Inj0 0)) (setsum 0 (setsum (x9 0) (setsum 0 0)))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 0) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . x0 (λ x14 x15 x16 . x14) 0) (λ x10 : (ι → ι → ι) → ι . x9 (λ x11 x12 . x10 (λ x13 x14 . 0))) x6 0)) (Inj0 0) (setsum x7 x7) = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x3 (λ x13 . λ x14 : ((ι → ι) → ι) → ι . λ x15 . 0) (λ x13 : (ι → ι) → ι → ι . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 . x3 (λ x18 . λ x19 : ((ι → ι) → ι) → ι . λ x20 . 0) (λ x18 : (ι → ι) → ι → ι . 0) 0) (λ x15 : (ι → ι) → ι → ι . x1 (λ x16 x17 . λ x18 : ι → ι . λ x19 . 0) (λ x16 : ι → ι → ι → ι . λ x17 x18 . 0) 0) (x14 (λ x15 x16 . 0))) (setsum (x0 (λ x14 x15 x16 . 0) 0) (x13 (λ x14 . 0) 0)) (setsum (setsum 0 0) (x0 (λ x14 x15 x16 . 0) 0))) (Inj0 (setsum (x2 (λ x13 x14 x15 : ι → ι . λ x16 . 0) (λ x13 : (ι → ι → ι) → ι . 0) 0 0) 0))) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x10) (x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (Inj0 (setsum 0 0)) 0) (λ x9 : (ι → ι → ι) → ι . x5) (Inj1 0) 0) = x2 (λ x9 x10 x11 : ι → ι . λ x12 . setsum (x9 (x11 x12)) 0) (λ x9 : (ι → ι → ι) → ι . setsum (setsum (x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . x9 (λ x13 x14 . 0)) (λ x10 : (ι → ι) → ι → ι . x9 (λ x11 x12 . 0)) 0) (x7 (λ x10 . setsum 0 0))) (setsum 0 0)) (setsum 0 (x7 (λ x9 . x6))) x6) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → ι) → ι . x1 (λ x9 x10 . λ x11 : ι → ι . setsum (x1 (λ x12 x13 . λ x14 : ι → ι . λ x15 . Inj0 x12) (λ x12 : ι → ι → ι → ι . λ x13 x14 . 0) (Inj1 (Inj1 0)))) (λ x9 : ι → ι → ι → ι . λ x10 x11 . Inj1 (x7 (λ x12 . 0))) 0 = x5 (λ x9 x10 . x2 (λ x11 x12 x13 : ι → ι . λ x14 . x12 (x2 (λ x15 x16 x17 : ι → ι . λ x18 . x1 (λ x19 x20 . λ x21 : ι → ι . λ x22 . 0) (λ x19 : ι → ι → ι → ι . λ x20 x21 . 0) 0) (λ x15 : (ι → ι → ι) → ι . Inj1 0) 0 (setsum 0 0))) (λ x11 : (ι → ι → ι) → ι . 0) (Inj1 0) 0) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 . x16) (λ x14 : (ι → ι) → ι → ι . x12 (λ x15 : ι → ι . x3 (λ x16 . λ x17 : ((ι → ι) → ι) → ι . λ x18 . 0) (λ x16 : (ι → ι) → ι → ι . 0) 0)) 0) (λ x11 : (ι → ι) → ι → ι . 0) (Inj1 (setsum (x1 (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) (λ x11 : ι → ι → ι → ι . λ x12 x13 . 0) 0) x10)))) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 x11 . 0) 0 = Inj0 (setsum (x1 (λ x9 x10 . λ x11 : ι → ι . λ x12 . x10) (λ x9 : ι → ι → ι → ι . λ x10 x11 . x7) 0) 0)) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → ι . ∀ x6 x7 . x0 (λ x9 x10 x11 . x2 (λ x12 x13 x14 : ι → ι . λ x15 . 0) (λ x12 : (ι → ι → ι) → ι . Inj1 (x0 (λ x13 x14 x15 . 0) 0)) 0 0) 0 = x2 (λ x9 x10 x11 : ι → ι . λ x12 . x0 (λ x13 x14 x15 . x15) (x11 (setsum (x11 0) (x10 0)))) (λ x9 : (ι → ι → ι) → ι . setsum (setsum 0 (Inj1 (x9 (λ x10 x11 . 0)))) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . x3 (λ x14 . λ x15 : ((ι → ι) → ι) → ι . λ x16 . Inj0 0) (λ x14 : (ι → ι) → ι → ι . x3 (λ x15 . λ x16 : ((ι → ι) → ι) → ι . λ x17 . 0) (λ x15 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0)) (λ x10 : (ι → ι → ι) → ι . x0 (λ x11 x12 x13 . x2 (λ x14 x15 x16 : ι → ι . λ x17 . 0) (λ x14 : (ι → ι → ι) → ι . 0) 0 0) (Inj1 0)) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . Inj1 0) (λ x10 : (ι → ι → ι) → ι . x3 (λ x11 . λ x12 : ((ι → ι) → ι) → ι . λ x13 . 0) (λ x11 : (ι → ι) → ι → ι . 0) 0) (setsum 0 0) (x2 (λ x10 x11 x12 : ι → ι . λ x13 . 0) (λ x10 : (ι → ι → ι) → ι . 0) 0 0)) (setsum (Inj1 0) (x0 (λ x10 x11 x12 . 0) 0)))) x4 (x2 (λ x9 x10 x11 : ι → ι . λ x12 . x1 (λ x13 x14 . λ x15 : ι → ι . λ x16 . x14) (λ x13 : ι → ι → ι → ι . λ x14 x15 . x12) x12) (λ x9 : (ι → ι → ι) → ι . Inj1 (setsum (setsum 0 0) 0)) 0 (x2 (λ x9 x10 x11 : ι → ι . λ x12 . 0) (λ x9 : (ι → ι → ι) → ι . x3 (λ x10 . λ x11 : ((ι → ι) → ι) → ι . λ x12 . Inj0 0) (λ x10 : (ι → ι) → ι → ι . x10 (λ x11 . 0) 0) 0) x4 0))) ⟶ False (proof)
Theorem ce3d6.. : ∀ x0 : ((ι → ι) → ι) → ι → ((ι → ι → ι) → ι) → ι . ∀ x1 : ((((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 → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 : ι → (ι → ι) → ι . x9 x5 (λ x10 . 0)) 0 (λ x9 . λ x10 : ι → ι . x9) (setsum (x0 (λ x9 : ι → ι . x9 (Inj1 0)) x4 (λ x9 : ι → ι → ι . 0)) 0) = x4) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 x6 x7 . x3 (λ x9 : ι → (ι → ι) → ι . 0) (Inj0 0) (λ x9 . λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι) → ι . setsum 0 (x11 0 (λ x12 . 0))) x6 (λ x11 . λ x12 : ι → ι . x1 (λ x13 : ((ι → ι) → ι → ι) → ι . 0) 0) (setsum x9 (x2 (λ x11 x12 x13 . λ x14 : ι → ι . x12) (λ x11 : ι → (ι → ι) → ι → ι . 0) x6))) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . setsum (x0 (λ x13 : ι → ι . setsum 0 0) (x0 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . 0)) (λ x13 : ι → ι → ι . 0)) (setsum x11 (x2 (λ x13 x14 x15 . λ x16 : ι → ι . 0) (λ x13 : ι → (ι → ι) → ι → ι . 0) 0))) (λ x9 : ι → (ι → ι) → ι → ι . 0) x5) = x2 (λ x9 x10 x11 . λ x12 : ι → ι . setsum x9 (Inj0 x9)) (λ x9 : ι → (ι → ι) → ι → ι . x5) x6) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x9) (λ x9 : ι → (ι → ι) → ι → ι . x6 (x6 (Inj0 (x3 (λ x10 : ι → (ι → ι) → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0) 0)) (setsum (x1 (λ x10 : ((ι → ι) → ι → ι) → ι . 0) 0) (x9 0 (λ x10 . 0) 0))) (setsum (Inj1 (x3 (λ x10 : ι → (ι → ι) → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0) 0)) (Inj0 (x5 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0)))) 0 = setsum (setsum 0 (x3 (λ x9 : ι → (ι → ι) → ι . x5 0 (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . 0) (Inj0 0)) (x3 (λ x9 : ι → (ι → ι) → ι . 0) (setsum 0 0) (λ x9 . λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι) → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0) 0) (setsum 0 0)) (λ x9 . λ x10 : ι → ι . 0) (Inj1 (Inj1 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . x2 (λ x9 x10 x11 . λ x12 : ι → ι . x2 (λ x13 x14 x15 . λ x16 : ι → ι . x15) (λ x13 : ι → (ι → ι) → ι → ι . x10) (x0 (λ x13 : ι → ι . Inj1 0) (x1 (λ x13 : ((ι → ι) → ι → ι) → ι . x10) (Inj0 0)) (λ x13 : ι → ι → ι . setsum 0 0))) (λ x9 : ι → (ι → ι) → ι → ι . x0 (λ x10 : ι → ι . setsum (x7 (setsum 0 0)) 0) (setsum 0 0) (λ x10 : ι → ι → ι . x1 (λ x11 : ((ι → ι) → ι → ι) → ι . x9 (x7 0) (λ x12 . 0) (x9 0 (λ x12 . 0) 0)) (x6 (λ x11 : ι → ι . 0)))) 0 = x0 (λ x9 : ι → ι . x3 (λ x10 : ι → (ι → ι) → ι . setsum (x7 0) (x1 (λ x11 : ((ι → ι) → ι → ι) → ι . x9 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . 0) 0))) (Inj1 (x6 (λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι) → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0) 0))) (λ x10 . λ x11 : ι → ι . x9 (x7 (setsum 0 0))) (x9 (x2 (λ x10 x11 x12 . λ x13 : ι → ι . Inj0 0) (λ x10 : ι → (ι → ι) → ι → ι . setsum 0 0) (x3 (λ x10 : ι → (ι → ι) → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0) 0)))) (setsum 0 (x2 (λ x9 x10 x11 . λ x12 : ι → ι . x11) (λ x9 : ι → (ι → ι) → ι → ι . Inj1 (Inj0 0)) (x7 0))) (λ x9 : ι → ι → ι . x3 (λ x10 : ι → (ι → ι) → ι . x2 (λ x11 x12 x13 . λ x14 : ι → ι . setsum (x0 (λ x15 : ι → ι . 0) 0 (λ x15 : ι → ι → ι . 0)) x13) (λ x11 : ι → (ι → ι) → ι → ι . Inj0 (x1 (λ x12 : ((ι → ι) → ι → ι) → ι . 0) 0)) (x9 (x3 (λ x11 : ι → (ι → ι) → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0) 0) 0)) (x6 (λ x10 : ι → ι . setsum (setsum 0 0) (x10 0))) (λ x10 . λ x11 : ι → ι . Inj0 (x9 0 0)) (setsum (x5 (x3 (λ x10 : ι → (ι → ι) → ι . 0) 0 (λ x10 . λ x11 : ι → ι . 0) 0)) (Inj0 (x2 (λ x10 x11 x12 . λ x13 : ι → ι . 0) (λ x10 : ι → (ι → ι) → ι → ι . 0) 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → ι → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . 0) 0 = x6) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x1 (λ x9 : ((ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι . λ x11 . x2 (λ x12 x13 x14 . λ x15 : ι → ι . Inj1 (x15 0)) (λ x12 : ι → (ι → ι) → ι → ι . x11) (Inj0 (Inj0 0)))) (x1 (λ x9 : ((ι → ι) → ι → ι) → ι . x7 (λ x10 . x7 (λ x11 . setsum 0 0) (λ x11 x12 . setsum 0 0) (λ x11 . x11)) (λ x10 x11 . x7 (λ x12 . x10) (λ x12 x13 . x13) (λ x12 . x11)) (λ x10 . Inj0 (x0 (λ x11 : ι → ι . 0) 0 (λ x11 : ι → ι → ι . 0)))) 0) = x1 (λ x9 : ((ι → ι) → ι → ι) → ι . setsum (x3 (λ x10 : ι → (ι → ι) → ι . x1 (λ x11 : ((ι → ι) → ι → ι) → ι . x3 (λ x12 : ι → (ι → ι) → ι . 0) 0 (λ x12 . λ x13 : ι → ι . 0) 0) 0) (x0 (λ x10 : ι → ι . Inj0 0) x6 (λ x10 : ι → ι → ι . x10 0 0)) (λ x10 . λ x11 : ι → ι . setsum (setsum 0 0) 0) (Inj0 (x9 (λ x10 : ι → ι . λ x11 . 0)))) (x5 x6)) x4) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → ι . 0) 0 (λ x9 : ι → ι → ι . 0) = Inj0 (Inj1 (x0 (λ x9 : ι → ι . x6 0 (setsum 0 0) (setsum 0 0) 0) 0 (λ x9 : ι → ι → ι . x0 (λ x10 : ι → ι . x3 (λ x11 : ι → (ι → ι) → ι . 0) 0 (λ x11 . λ x12 : ι → ι . 0) 0) 0 (λ x10 : ι → ι → ι . x7 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι → ι → ι) → ((ι → ι) → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → ι . 0) (x0 (λ x9 : ι → ι . setsum 0 0) x5 (λ x9 : ι → ι → ι . setsum 0 (x7 0))) (λ x9 : ι → ι → ι . x5) = Inj1 (setsum (Inj1 (x2 (λ x9 x10 x11 . λ x12 : ι → ι . x10) (λ x9 : ι → (ι → ι) → ι → ι . 0) 0)) x5)) ⟶ False (proof)
Theorem 281bb.. : ∀ x0 : (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) → (ι → (ι → ι) → ι) → ι . ∀ x3 : (((ι → (ι → ι) → ι) → ι → ι) → ι) → (((ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι) → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι) → ι → ι) → ι → ι → ι → ι . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x9 (λ x10 . λ x11 : ι → ι . x11 (x2 (λ x12 . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . Inj1 0) (λ x12 . λ x13 : ι → ι . 0))) (x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . Inj1 (Inj0 0)) (x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x1 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0)) (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x2 (λ x10 . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . λ x11 : ι → ι . 0))) (x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . 0) (x0 (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . 0) 0 0 0) (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (x9 (λ x10 . λ x11 : ι → ι . 0) 0)) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x12) = x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x3 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x10 (setsum (x2 (λ x12 . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι . 0)) (setsum 0 0))) (λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . Inj1 0)) (setsum 0 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . setsum 0 0) (Inj1 0) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x9 (λ x10 . λ x11 : ι → ι . 0) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) (Inj0 (x5 (x4 (λ x9 . x5 0)))) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x10 x11 x12 x13 . x1 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x15 x16 . λ x17 : ι → ι . 0)) (λ x14 x15 . λ x16 : ι → ι . setsum 0 0)) (λ x10 : ι → ι . x0 (λ x11 x12 x13 x14 . x2 (λ x15 . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . λ x19 . 0) (λ x15 . λ x16 : ι → ι . 0)) (λ x11 : ι → ι . x2 (λ x12 . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι . 0)) (Inj0 0) (x10 0) 0) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . Inj1 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . setsum 0 0)) (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x6 (λ x11 : ι → ι . λ x12 . 0) 0 0 0) (λ x10 x11 . λ x12 : ι → ι . setsum 0 0)) (x0 (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . 0) (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0)) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0)))) (λ x9 x10 . λ x11 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → (ι → ι) → ι . x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x5 0 (λ x10 : ι → ι . λ x11 . x3 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0))) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10) = x5 x4 (λ x9 : ι → ι . λ x10 . x2 (λ x11 . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . λ x12 : ι → ι . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x9 . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : ι → ι . x10 0) = x7 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι → ι → ι . x2 (λ x9 . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : ι → ι . 0) = Inj0 (Inj1 (x0 (λ x9 x10 x11 x12 . x1 (λ x13 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x13 x14 . λ x15 : ι → ι . 0)) (λ x9 : ι → ι . setsum 0 (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) (x7 (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . 0)) (x7 0 0 0) (setsum 0 0)) (setsum (x6 (λ x9 : ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0)) (x7 0 0 0)) (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . Inj1 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 x7 . x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . Inj1 (Inj1 (x2 (λ x11 . λ x12 : (ι → ι → ι) → (ι → ι) → ι . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 . λ x12 : ι → ι . 0)))) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x10 (λ x14 . x14) (setsum 0 (x0 (λ x14 x15 x16 x17 . 0) (λ x14 : ι → ι . 0) 0 0 0)))) (λ x9 x10 . λ x11 : ι → ι . 0) = x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . setsum x7 (x0 (λ x11 x12 x13 x14 . x1 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x15 x16 . λ x17 : ι → ι . 0)) (λ x11 : ι → ι . x9 (λ x12 . λ x13 : ι → ι . 0) 0) (Inj0 0) 0 (Inj1 0))) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x0 (λ x14 x15 x16 x17 . x17) (λ x14 : ι → ι . x14 0) 0 (x3 (λ x14 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x14 : (ι → ι) → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x18 x19 . λ x20 : ι → ι . 0))) 0)) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x1 (λ x13 : ((ι → ι → ι) → (ι → ι) → ι) → ι . Inj0 0) (λ x13 x14 . λ x15 : ι → ι . setsum x12 x13))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . setsum (x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . setsum (setsum 0 0) (x1 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0))) (λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x13 x14 . λ x15 : ι → ι . x0 (λ x16 x17 x18 x19 . 0) (λ x16 : ι → ι . 0) 0 0 0))) (x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . x6) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13))) (λ x9 x10 . λ x11 : ι → ι . 0) = x5) ⟶ (∀ x4 x5 : ι → ι → ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι → ι . ∀ x7 . x0 (λ x9 x10 x11 x12 . setsum 0 x9) (λ x9 : ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . x0 (λ x11 x12 x13 x14 . x11) (λ x11 : ι → ι . Inj1 0) (Inj1 (setsum 0 0)) 0 0) (λ x10 x11 . x11) (Inj0 (x9 (setsum 0 0)))) 0 (x0 (λ x9 x10 x11 x12 . x9) (λ x9 : ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 x11 . 0) (Inj0 (x2 (λ x10 . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . λ x11 : ι → ι . 0)))) x7 (setsum x7 0) (setsum (x6 (λ x9 : (ι → ι) → ι → ι . x2 (λ x10 . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . λ x11 : ι → ι . 0)) (λ x9 x10 . Inj0 0) (x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0)) 0)) (x4 (Inj1 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . Inj0 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) (Inj0 (x0 (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 x11 . 0) 0) (Inj0 0) (Inj0 0) 0)) (x5 (setsum (Inj0 0) (setsum 0 0)) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . setsum 0 0)) (setsum (Inj1 0) x7) (Inj1 0)) (setsum (x0 (λ x9 x10 x11 x12 . x10) (λ x9 : ι → ι . x3 (λ x10 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)) (x0 (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . 0) 0 0 0) x7 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0))) (setsum x7 0))) = x4 (x0 (λ x9 x10 x11 x12 . Inj1 (setsum (x2 (λ x13 . λ x14 : (ι → ι → ι) → (ι → ι) → ι . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 . λ x14 : ι → ι . 0)) x9)) (λ x9 : ι → ι . x0 (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . x6 (λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x11 x12 . x1 (λ x13 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x13 x14 . λ x15 : ι → ι . 0)) (x3 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0))) (x6 (λ x10 : (ι → ι) → ι → ι . x3 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0)) (λ x10 x11 . x2 (λ x12 . λ x13 : (ι → ι → ι) → (ι → ι) → ι . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . λ x16 . 0) (λ x12 . λ x13 : ι → ι . 0)) (Inj0 0)) (x2 (λ x10 . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . λ x11 : ι → ι . x0 (λ x12 x13 x14 x15 . 0) (λ x12 : ι → ι . 0) 0 0 0)) 0) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . x11 (Inj0 0))) (x4 (Inj1 (x2 (λ x9 . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 . λ x10 : ι → ι . 0))) (x4 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (Inj0 0) (Inj1 0) (setsum 0 0)) (setsum (setsum 0 0) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . 0))) (x2 (λ x9 . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . setsum 0 0) (λ x9 . λ x10 : ι → ι . setsum 0 0))) 0) (setsum (x4 x7 (x6 (λ x9 : (ι → ι) → ι → ι . x9 (λ x10 . 0) 0) (λ x9 x10 . setsum 0 0) (x5 0 0 0 0)) (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . x0 (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . 0) 0 0 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . x10)) (Inj0 0)) (Inj0 0)) (x4 (x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) 0 (x4 (setsum (x5 0 0 0 0) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . 0))) (x4 (x3 (λ x9 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0)) (x6 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) (setsum 0 0) 0) 0 x7) (Inj0 (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x2 (λ x10 . λ x11 : (ι → ι → ι) → (ι → ι) → ι . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 . λ x11 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . setsum 0 0)))) (x2 (λ x9 . λ x10 : (ι → ι → ι) → (ι → ι) → ι . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . x12 (x2 (λ x14 . λ x15 : (ι → ι → ι) → (ι → ι) → ι . λ x16 : (ι → ι) → ι . λ x17 : ι → ι . λ x18 . 0) (λ x14 . λ x15 : ι → ι . x1 (λ x16 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x16 x17 . λ x18 : ι → ι . 0)))) (λ x9 . λ x10 : ι → ι . x1 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x10 x7) (λ x11 x12 . λ x13 : ι → ι . 0)))) ⟶ (∀ x4 : ((ι → ι → ι) → ι → ι → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι → ι) → ι . x0 (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . setsum (x9 (x7 (λ x10 : (ι → ι) → ι . λ x11 . 0))) (Inj1 (x9 0))) 0 (x4 (λ x9 : ι → ι → ι . λ x10 x11 . 0) (λ x9 . x7 (λ x10 : (ι → ι) → ι . λ x11 . 0)) (λ x9 . 0) x6) (x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . Inj0 (setsum 0 (x7 (λ x10 : (ι → ι) → ι . λ x11 . 0)))) (λ x9 x10 . λ x11 : ι → ι . x7 (λ x12 : (ι → ι) → ι . λ x13 . x1 (λ x14 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x11 0) (λ x14 x15 . λ x16 : ι → ι . 0)))) = x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x1 (λ x10 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x0 (λ x11 x12 x13 x14 . x1 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x2 (λ x16 . λ x17 : (ι → ι → ι) → (ι → ι) → ι . λ x18 : (ι → ι) → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 . λ x17 : ι → ι . 0)) (λ x15 x16 . λ x17 : ι → ι . 0)) (λ x11 : ι → ι . x11 (Inj1 0)) (x9 (λ x11 : ι → ι → ι . λ x12 : ι → ι . x12 0)) (x3 (λ x11 : (ι → (ι → ι) → ι) → ι → ι . x3 (λ x12 : (ι → (ι → ι) → ι) → ι → ι . 0) (λ x12 : (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (λ x11 : (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 . λ x16 : (ι → ι → ι) → (ι → ι) → ι . λ x17 : (ι → ι) → ι . λ x18 : ι → ι . λ x19 . 0) (λ x15 . λ x16 : ι → ι . 0))) (x1 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι) → ι . x9 (λ x12 : ι → ι → ι . λ x13 : ι → ι . 0)) (λ x11 x12 . λ x13 : ι → ι . 0))) (λ x10 x11 . λ x12 : ι → ι . 0)) (λ x9 x10 . λ x11 : ι → ι . x1 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι) → ι . 0) (λ x12 x13 . λ x14 : ι → ι . 0))) ⟶ False (proof)
Theorem ff51f.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → ι) → ι → ((ι → ι) → ι → ι) → ι . ∀ x2 : ((ι → ι) → ι) → ι → ι . ∀ x3 : ((ι → ((ι → ι) → ι → ι) → ι) → ι) → ι → ι . (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (ι → ι → ι → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x7 (λ x10 x11 x12 . 0)) 0 = Inj1 (x1 (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (x0 (λ x10 . Inj0 0) (x0 (λ x10 . 0) 0))) (λ x9 . setsum (x1 (λ x10 . Inj0 0) (λ x10 . Inj1 0) x6 (λ x10 : ι → ι . λ x11 . 0)) (x7 (λ x10 x11 x12 . setsum 0 0))) x4 (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ι . x2 (λ x12 : ι → ι . 0) (Inj0 0)) (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 (λ x12 : ι → ι . λ x13 . 0)) (Inj0 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x2 (λ x10 : ι → ι . Inj1 (setsum 0 (x2 (λ x11 : ι → ι . 0) 0))) (x7 (λ x10 x11 x12 . x9 x10 (λ x13 : ι → ι . λ x14 . setsum 0 0)))) (x1 (λ x9 . x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) (x2 (λ x10 : ι → ι . 0) (Inj0 0))) (λ x9 . 0) x5 (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ι . x9 (x7 (λ x12 x13 x14 . 0))) (x2 (λ x11 : ι → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 (λ x12 : ι → ι . λ x13 . 0)) 0))) = x2 (λ x9 : ι → ι . x2 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . x0 (λ x12 . x10 0) (setsum 0 0)) 0) (setsum (x6 (λ x10 x11 . setsum 0 0) (λ x10 x11 . 0) (λ x10 . x10) (x6 (λ x10 x11 . 0) (λ x10 x11 . 0) (λ x10 . 0) 0)) (x2 (λ x10 : ι → ι . x9 0) (x9 0)))) (setsum 0 (x6 (λ x9 x10 . 0) (λ x9 x10 . Inj1 (x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . 0) 0)) (λ x9 . Inj0 (Inj0 0)) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι . Inj1 (x2 (λ x10 : ι → ι . x3 (λ x11 : ι → ((ι → ι) → ι → ι) → ι . x1 (λ x12 . 0) (λ x12 . 0) 0 (λ x12 : ι → ι . λ x13 . 0)) (x10 0)) (x9 0))) (x0 (λ x9 . 0) 0) = x0 (λ x9 . setsum (x0 (λ x10 . Inj0 (setsum 0 0)) (Inj1 (setsum 0 0))) x5) x5) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ι . setsum x7 (Inj0 (x5 (λ x10 x11 . 0) (x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (λ x10 . 0) 0))) (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) (x5 (λ x9 x10 . x2 (λ x11 : ι → ι . x9) (Inj0 0)) (setsum (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . 0) 0) (x2 (λ x9 : ι → ι . 0) 0)) (λ x9 . 0) (x4 (λ x9 : (ι → ι) → ι . λ x10 . x10) (λ x9 : ι → ι . λ x10 . x0 (λ x11 . 0) 0) (λ x9 . setsum 0 0) (Inj1 0)))) = Inj0 (x3 (λ x9 : ι → ((ι → ι) → ι → ι) → ι . x2 (λ x10 : ι → ι . x0 (λ x11 . 0) (x1 (λ x11 . 0) (λ x11 . 0) 0 (λ x11 : ι → ι . λ x12 . 0))) 0) (x6 (λ x9 : (ι → ι) → ι . 0)))) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . 0) (λ x9 . x9) (x2 (λ x9 : ι → ι . x0 (λ x10 . x9 (x2 (λ x11 : ι → ι . 0) 0)) (setsum (setsum 0 0) (setsum 0 0))) (x2 (λ x9 : ι → ι . x6 (Inj0 0) (λ x10 . x2 (λ x11 : ι → ι . 0) 0) (Inj0 0)) (setsum 0 (x0 (λ x9 . 0) 0)))) (λ x9 : ι → ι . λ x10 . 0) = x2 (λ x9 : ι → ι . setsum (setsum 0 (Inj1 0)) (x1 (λ x10 . 0) (λ x10 . x7) 0 (λ x10 : ι → ι . λ x11 . setsum 0 (x10 0)))) (x0 (λ x9 . setsum x9 0) x4)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : (ι → ι → ι) → (ι → ι) → ι → ι → ι . x1 (λ x9 . x6 (λ x10 : (ι → ι) → ι . x0 (λ x11 . x0 (λ x12 . 0) (x0 (λ x12 . 0) 0)) (setsum 0 0))) (λ x9 . 0) 0 (λ x9 : ι → ι . λ x10 . x0 (λ x11 . 0) (x1 (λ x11 . 0) (λ x11 . 0) (setsum (x1 (λ x11 . 0) (λ x11 . 0) 0 (λ x11 : ι → ι . λ x12 . 0)) (Inj1 0)) (λ x11 : ι → ι . λ x12 . x0 (λ x13 . 0) x10))) = x0 (λ x9 . setsum (Inj1 (setsum 0 (setsum 0 0))) (x1 Inj1 (λ x10 . setsum 0 (x1 (λ x11 . 0) (λ x11 . 0) 0 (λ x11 : ι → ι . λ x12 . 0))) (x0 (λ x10 . x10) (Inj1 0)) (λ x10 : ι → ι . λ x11 . x3 (λ x12 : ι → ((ι → ι) → ι → ι) → ι . setsum 0 0) (x2 (λ x12 : ι → ι . 0) 0)))) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0))) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 . x0 (λ x9 . 0) (Inj0 (x4 (λ x9 . Inj0 0) (λ x9 . 0))) = x5) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x0 (λ x9 . x1 (λ x10 . x6) (x0 (λ x10 . x1 (λ x11 . Inj0 0) (λ x11 . 0) (x0 (λ x11 . 0) 0) (λ x11 : ι → ι . λ x12 . x1 (λ x13 . 0) (λ x13 . 0) 0 (λ x13 : ι → ι . λ x14 . 0)))) (Inj1 (setsum 0 (x5 0))) (λ x10 : ι → ι . λ x11 . x1 (λ x12 . setsum (x10 0) (x1 (λ x13 . 0) (λ x13 . 0) 0 (λ x13 : ι → ι . λ x14 . 0))) (λ x12 . x3 (λ x13 : ι → ((ι → ι) → ι → ι) → ι . x13 0 (λ x14 : ι → ι . λ x15 . 0)) 0) (x2 (λ x12 : ι → ι . x12 0) (x7 0)) (λ x12 : ι → ι . λ x13 . 0))) (x5 (Inj1 0)) = x5 (x1 (λ x9 . x5 (x3 (λ x10 : ι → ((ι → ι) → ι → ι) → ι . Inj1 0) (x5 0))) (λ x9 . x7 0) 0 (λ x9 : ι → ι . λ x10 . x9 0))) ⟶ False (proof)
Theorem 3f800.. : ∀ 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 . ∀ x3 : (ι → ι) → ι → ι → ι . (∀ x4 : (((ι → ι) → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι → ι . x3 (λ x9 . x7 (λ x10 : ι → ι → ι . λ x11 . 0) (x3 (λ x10 . x6) x9 (Inj1 0))) (x2 (λ x9 . x3 (λ x10 . 0) (setsum (x3 (λ x10 . 0) 0 0) 0) (x3 (λ x10 . x2 (λ x11 . 0) 0) x5 (x2 (λ x10 . 0) 0))) (x4 (λ x9 : (ι → ι) → ι . x9 (λ x10 . x0 (λ x11 : ι → ι → ι . 0) 0 (λ x11 . 0))))) x6 = setsum 0 (x4 (λ x9 : (ι → ι) → ι . Inj1 x6))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 . setsum x9 x9) (x4 (x5 (λ x9 : (ι → ι) → ι . 0))) (Inj0 (x2 (λ x9 . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . setsum 0 0) (λ x10 : ι → ι . x9) (λ x10 : (ι → ι) → ι . x6) (setsum 0 0)) (x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . setsum 0 0) (λ x9 : ι → ι . x3 (λ x10 . 0) 0 0) (λ x9 : (ι → ι) → ι . x2 (λ x10 . 0) 0) 0))) = x4 (x7 0)) ⟶ (∀ x4 : (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 x7 : ι → ι . x2 (λ x9 . x2 (λ x10 . x9) 0) (x2 (λ x9 . 0) (x5 (Inj0 (x2 (λ x9 . 0) 0)) (λ x9 : ι → ι . x7 (x3 (λ x10 . 0) 0 0)) (λ x9 . x3 (λ x10 . 0) (x6 0) 0))) = x2 (λ x9 . Inj0 (setsum x9 (setsum x9 0))) (setsum 0 (x4 (λ x9 . x3 (λ x10 . Inj0 0) (x5 0 (λ x10 : ι → ι . 0) (λ x10 . 0)) (x7 0)) (λ x9 . x3 (λ x10 . 0) (x5 0 (λ x10 : ι → ι . 0) (λ x10 . 0)) (x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 . 0)))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : ι → ι → ι → ι . x2 (λ x9 . 0) 0 = x5) ⟶ (∀ x4 : (ι → ι → ι) → (ι → ι → ι) → ι . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x10 (λ x12 x13 . setsum (x0 (λ x14 : ι → ι → ι . Inj0 0) x12 (λ x14 . x3 (λ x15 . 0) 0 0)) (x3 (λ x14 . x12) (setsum 0 0) (x10 (λ x14 x15 . 0) 0))) 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . x5 (λ x10 : ι → ι . 0) (x0 (λ x10 : ι → ι → ι . 0) (setsum 0 (x7 (λ x10 . λ x11 : ι → ι . λ x12 . 0))) (λ x10 . x9 (λ x11 . 0))) (λ x10 . x10)) (setsum (x7 (λ x9 . λ x10 : ι → ι . λ x11 . x11)) 0) = Inj0 (Inj1 (x5 (λ x9 : ι → ι . x3 (λ x10 . 0) (x2 (λ x10 . 0) 0) (x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 . 0))) (Inj0 (x4 (λ x9 x10 . 0) (λ x9 x10 . 0))) (λ x9 . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . Inj1 0) (λ x10 : ι → ι . setsum 0 0) (λ x10 : (ι → ι) → ι . Inj0 0) 0)))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x2 (λ x12 . Inj0 0) x9) (λ x9 : ι → ι . x0 (λ x10 : ι → ι → ι . setsum 0 (setsum (x2 (λ x11 . 0) 0) 0)) 0 (λ x10 . Inj0 (setsum (Inj0 0) 0))) (λ x9 : (ι → ι) → ι . 0) (x3 (x2 (λ x9 . x9)) (x2 (λ x9 . x6 (λ x10 . x0 (λ x11 : ι → ι → ι . 0) 0 (λ x11 . 0))) (x7 (λ x9 . 0) 0 (λ x9 . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0) 0)) (x3 (λ x9 . x5) 0 0)) = setsum (setsum (x3 (λ x9 . x5) x5 (setsum (x4 (λ x9 . λ x10 : ι → ι . 0)) (x6 (λ x9 . 0)))) (x3 (λ x9 . 0) (setsum (x0 (λ x9 : ι → ι → ι . 0) 0 (λ x9 . 0)) 0) (setsum (x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . 0) (λ x9 : ι → ι . 0) (λ x9 : (ι → ι) → ι . 0) 0) (x7 (λ x9 . 0) 0 (λ x9 . 0) 0)))) (x4 (λ x9 . λ x10 : ι → ι . setsum (x6 (λ x11 . setsum 0 0)) 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : ι → ι → ι → ι → ι . x0 (λ x9 : ι → ι → ι . x5) (x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . Inj1 (x3 (λ x12 . 0) 0 (x1 (λ x12 . λ x13 : (ι → ι → ι) → ι → ι . λ x14 . 0) (λ x12 : ι → ι . 0) (λ x12 : (ι → ι) → ι . 0) 0))) (λ x9 : ι → ι . Inj0 (x2 (λ x10 . x10) (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . 0) (λ x10 : ι → ι . 0) (λ x10 : (ι → ι) → ι . 0) 0))) (λ x9 : (ι → ι) → ι . 0) (x3 (λ x9 . 0) 0 (x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . Inj0 0) (λ x9 : ι → ι . x0 (λ x10 : ι → ι → ι . 0) 0 (λ x10 . 0)) (λ x9 : (ι → ι) → ι . Inj0 0) 0))) (λ x9 . x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . x12) (λ x10 : ι → ι . x1 (λ x11 . λ x12 : (ι → ι → ι) → ι → ι . λ x13 . Inj1 (x3 (λ x14 . 0) 0 0)) (λ x11 : ι → ι . x9) (λ x11 : (ι → ι) → ι . x0 (λ x12 : ι → ι → ι . x1 (λ x13 . λ x14 : (ι → ι → ι) → ι → ι . λ x15 . 0) (λ x13 : ι → ι . 0) (λ x13 : (ι → ι) → ι . 0) 0) 0 (λ x12 . 0)) (setsum (x2 (λ x11 . 0) 0) (x7 0 0 0 0))) (λ x10 : (ι → ι) → ι . 0) (Inj0 (x2 (λ x10 . Inj1 0) 0))) = x1 (λ x9 . λ x10 : (ι → ι → ι) → ι → ι . λ x11 . x9) (λ x9 : ι → ι . x3 (λ x10 . x9 (setsum 0 0)) (setsum 0 (x1 (λ x10 . λ x11 : (ι → ι → ι) → ι → ι . λ x12 . x3 (λ x13 . 0) 0 0) (λ x10 : ι → ι . x1 (λ x11 . λ x12 : (ι → ι → ι) → ι → ι . λ x13 . 0) (λ x11 : ι → ι . 0) (λ x11 : (ι → ι) → ι . 0) 0) (λ x10 : (ι → ι) → ι . x3 (λ x11 . 0) 0 0) 0)) 0) (λ x9 : (ι → ι) → ι . Inj1 (x0 (λ x10 : ι → ι → ι . x3 (λ x11 . x2 (λ x12 . 0) 0) (x2 (λ x11 . 0) 0) (x3 (λ x11 . 0) 0 0)) 0 (λ x10 . x1 (λ x11 . λ x12 : (ι → ι → ι) → ι → ι . λ x13 . Inj0 0) (λ x11 : ι → ι . Inj0 0) (λ x11 : (ι → ι) → ι . x3 (λ x12 . 0) 0 0) (Inj1 0)))) (Inj0 x5)) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 : ι → ι . x0 (λ x9 : ι → ι → ι . 0) (x7 (x3 (λ x9 . x2 (λ x10 . x3 (λ x11 . 0) 0 0) (Inj0 0)) (setsum 0 x5) 0)) (λ x9 . x9) = x7 (setsum 0 0)) ⟶ False (proof)
Theorem 1823d.. : ∀ x0 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι . ∀ x1 : (ι → 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 . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . x3 (λ x9 . Inj0 (setsum 0 (Inj1 x9))) (setsum 0 x4) (λ x9 : (ι → ι) → ι . x5) = setsum (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x0 (λ x12 x13 : ι → ι . Inj1 (setsum 0 0)) (Inj1 0) (x0 (λ x12 x13 : ι → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0)) (Inj0 0) (x7 0 (λ x12 : ι → ι . λ x13 . 0) (λ x12 . 0)))) (λ x9 x10 . 0) (setsum x5 (x7 x4 (λ x9 : ι → ι . λ x10 . x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)) (λ x9 . x6 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . x3 (λ x9 . x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . x2 (λ x14 : ι → ι → ι . λ x15 . x3 (λ x16 . 0) 0 (λ x16 : (ι → ι) → ι . 0)) (setsum 0 0) (λ x14 x15 . x12 (λ x16 . 0) 0)) (x0 (λ x13 x14 : ι → ι . x13 0) (setsum 0 0) x11)) (λ x10 . Inj0) (x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . x3 (λ x13 . 0) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0)) (λ x13 : (ι → ι) → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0))) (λ x10 x11 . x0 (λ x12 x13 : ι → ι . x2 (λ x14 : ι → ι → ι . λ x15 . 0) 0 (λ x14 x15 . 0)) (x0 (λ x12 x13 : ι → ι . 0) 0 0) (setsum 0 0)) (Inj0 x9))) x6 (λ x9 : (ι → ι) → ι . Inj1 0) = Inj0 (x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . x3 (λ x11 . Inj1 (Inj0 0)) 0 (λ x11 : (ι → ι) → ι . Inj1 (x10 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . x2 (λ x9 : ι → ι → ι . λ x10 . setsum 0 (x7 (x0 (λ x11 x12 : ι → ι . x0 (λ x13 x14 : ι → ι . 0) 0 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (λ x11 : ι → ι . λ x12 . Inj0 (Inj1 0)))) (x7 (λ x9 . x5) (λ x9 : ι → ι . λ x10 . setsum (x3 (λ x11 . x3 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι . 0)) 0 (λ x11 : (ι → ι) → ι . 0)) x6)) (λ x9 x10 . setsum 0 0) = x7 (λ x9 . x6) (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 : ι → ι → ι . λ x12 . x3 (λ x13 . setsum 0 0) (setsum 0 0) (λ x13 : (ι → ι) → ι . 0)) (Inj0 0) (λ x11 x12 . x9 (setsum 0 0))) (x3 (λ x11 . x3 (λ x12 . Inj1 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0) 0) (λ x12 : (ι → ι) → ι . 0)) (Inj0 x6) (λ x11 : (ι → ι) → ι . x2 (λ x12 : ι → ι → ι . λ x13 . setsum 0 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 x13 . 0) 0) (λ x12 x13 . 0))))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 : ι → ι → ι . λ x10 . x7) x5 (λ x9 x10 . x0 (λ x11 x12 : ι → ι . x11 (x2 (λ x13 : ι → ι → ι . λ x14 . setsum 0 0) 0 (λ x13 x14 . setsum 0 0))) 0 (x2 (λ x11 : ι → ι → ι . λ x12 . setsum (x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . 0)) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0))) (setsum (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)) (x6 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 : ι → ι . 0) (λ x11 . 0) 0)) (λ x11 x12 . x0 (λ x13 x14 : ι → ι . x13 0) (x2 (λ x13 : ι → ι → ι . λ x14 . 0) 0 (λ x13 x14 . 0)) (x0 (λ x13 x14 : ι → ι . 0) 0 0)))) = x0 (λ x9 x10 : ι → ι . x7) (x2 (λ x9 : ι → ι → ι . λ x10 . setsum (setsum (Inj1 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)) 0) 0 (λ x9 x10 . x3 (λ x11 . 0) x10 (λ x11 : (ι → ι) → ι . x10))) x5) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . setsum (setsum (Inj0 (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (setsum 0 (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0)))) (setsum (x7 (x2 (λ x11 : ι → ι → ι . λ x12 . 0) 0 (λ x11 x12 . 0))) x9)) (x3 (λ x9 . x3 (λ x10 . 0) x5 (λ x10 : (ι → ι) → ι . x9)) (Inj1 (Inj1 (setsum 0 0))) (λ x9 : (ι → ι) → ι . x2 (λ x10 : ι → ι → ι . λ x11 . x10 (x0 (λ x12 x13 : ι → ι . 0) 0 0) (Inj0 0)) 0 (λ x10 x11 . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . setsum 0 0) (λ x12 x13 . Inj0 0) (setsum 0 0)))) = Inj1 (Inj1 x6)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x5 x6 x7 . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0 = x7) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι → ι . x0 (λ x9 x10 : ι → ι . x7 (Inj0 0) (x9 (x2 (λ x11 : ι → ι → ι . λ x12 . Inj0 0) (x1 (λ x11 x12 . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 x12 . 0) 0) (λ x11 x12 . x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (λ x13 x14 . 0) 0))) (λ x11 . x0 (λ x12 x13 : ι → ι . 0) (x2 (λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x12 x13 . 0)) (x2 (λ x12 : ι → ι → ι . λ x13 . x12 0 0) (Inj0 0) (λ x12 x13 . x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . 0) (λ x14 x15 . 0) 0))) (x0 (λ x11 x12 : ι → ι . Inj0 (setsum 0 0)) (x10 (x0 (λ x11 x12 : ι → ι . 0) 0 0)) (x0 (λ x11 x12 : ι → ι . x11 0) (x9 0) (x0 (λ x11 x12 : ι → ι . 0) 0 0)))) 0 0 = setsum (setsum (setsum x5 (x2 (λ x9 : ι → ι → ι . λ x10 . x3 (λ x11 . 0) 0 (λ x11 : (ι → ι) → ι . 0)) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) (λ x9 x10 . x9))) 0) (x7 (setsum (x7 (setsum 0 0) (x7 0 0 (λ x9 . 0) 0) (λ x9 . x1 (λ x10 x11 . λ x12 : (ι → ι) → ι → ι . 0) (λ x10 x11 . 0) 0) 0) (x0 (λ x9 x10 : ι → ι . x6 0 0) (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (setsum 0 0))) (x6 0 (setsum (x0 (λ x9 x10 : ι → ι . 0) 0 0) (setsum 0 0))) (λ x9 . x2 (λ x10 : ι → ι → ι . λ x11 . x0 (λ x12 x13 : ι → ι . 0) 0 (x2 (λ x12 : ι → ι → ι . λ x13 . 0) 0 (λ x12 x13 . 0))) 0 (λ x10 x11 . x7 x9 (x3 (λ x12 . 0) 0 (λ x12 : (ι → ι) → ι . 0)) (λ x12 . 0) 0)) (Inj0 (x7 (x3 (λ x9 . 0) 0 (λ x9 : (ι → ι) → ι . 0)) (x0 (λ x9 x10 : ι → ι . 0) 0 0) (λ x9 . x7 0 0 (λ x10 . 0) 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι . x0 (λ x9 x10 : ι → ι . 0) 0 0 = x7 (x0 (λ x9 x10 : ι → ι . x9 (x0 (λ x11 x12 : ι → ι . x12 0) (Inj0 0) (x6 0))) (Inj1 0) (x0 (λ x9 x10 : ι → ι . x0 (λ x11 x12 : ι → ι . x3 (λ x13 . 0) 0 (λ x13 : (ι → ι) → ι . 0)) 0 (x10 0)) x5 (x4 (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0) (λ x9 : ι → ι . λ x10 . setsum 0 0) (λ x9 . 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0)))) (λ x9 : ι → ι . λ x10 . x3 (λ x11 . x11) (Inj0 (setsum (setsum 0 0) (Inj1 0))) (λ x11 : (ι → ι) → ι . 0))) ⟶ False (proof)
Theorem ebf15.. : ∀ x0 : (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) → 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 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x6 (Inj1 x7)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) = Inj1 (setsum (x3 (λ x9 . x9) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 (x10 0 0))) (Inj0 (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . 0))))) ⟶ (∀ x4 : (ι → ι) → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι → ι) → ι . x3 (λ x9 . x9) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) = Inj1 0) ⟶ (∀ x4 : (ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 . setsum x7 0) (λ x9 : ι → ι → ι . λ x10 . x0 (λ x11 x12 . x12) 0 (λ x11 . λ x12 : ι → ι . Inj0 x11)) = x0 (λ x9 x10 . Inj1 0) (x5 (λ x9 . λ x10 : ι → ι . λ x11 . 0) (λ x9 : ι → ι . λ x10 . x10)) (λ x9 . λ x10 : ι → ι . Inj1 (x1 (λ x11 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . x1 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj0 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (λ x11 : ι → ι . λ x12 . λ x13 : ι → ι . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → (ι → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x2 (λ x9 x10 x11 . x11) (λ x9 : ι → ι → ι . λ x10 . 0) = x6 (λ x9 : (ι → ι) → ι → ι . λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . λ x12 . x3 (λ x13 . 0) (λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x3 (λ x17 . 0) (λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 (x6 (λ x10 . x7) (setsum 0 x5) (λ x10 . setsum (x2 (λ x11 x12 x13 . 0) (λ x11 : ι → ι → ι . λ x12 . 0)) (setsum 0 0)))) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (Inj1 0) (x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum (x13 0 0) (x2 (λ x16 x17 x18 . 0) (λ x16 : ι → ι → ι . λ x17 . 0))))) = setsum (Inj1 x7) (Inj1 (setsum (x4 (x6 (λ x9 . 0) 0 (λ x9 . 0))) (x3 (λ x9 . x0 (λ x10 x11 . 0) 0 (λ x10 . λ x11 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . setsum 0 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 : ι → ι . x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . setsum (x1 (λ x12 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x12 : ι → ι . λ x13 . λ x14 : ι → ι . 0)) (x7 (Inj0 (x11 0)))) = setsum (x1 (λ x9 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . Inj1 0) (λ x9 : ι → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) (λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x12 (x14 0)))) (x7 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x0 (λ x9 x10 . setsum (x0 (λ x11 x12 . 0) (Inj0 (x2 (λ x11 x12 x13 . 0) (λ x11 : ι → ι → ι . λ x12 . 0))) (λ x11 . λ x12 : ι → ι . Inj1 (x2 (λ x13 x14 x15 . 0) (λ x13 : ι → ι → ι . λ x14 . 0)))) 0) x5 (λ x9 . λ x10 : ι → ι . x7) = Inj0 x5) ⟶ (∀ x4 : ι → ι → (ι → ι) → ι . ∀ x5 : (ι → ι → ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → (ι → ι) → ι) → ι → ι → ι → ι . x0 (λ x9 x10 . x9) (Inj1 (Inj0 (x2 (λ x9 x10 x11 . setsum 0 0) (λ x9 : ι → ι → ι . λ x10 . 0)))) (λ x9 . λ x10 : ι → ι . 0) = setsum x6 (x7 (λ x9 x10 : ι → ι . x0 (λ x11 x12 . x2 (λ x13 x14 x15 . x14) (λ x13 : ι → ι → ι . λ x14 . 0)) x6 (λ x11 . λ x12 : ι → ι . Inj1 (x9 0))) (Inj0 0) 0 (x7 (λ x9 x10 : ι → ι . x0 (λ x11 x12 . x1 (λ x13 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x13 : ι → ι . λ x14 . λ x15 : ι → ι . 0)) (setsum 0 0) (λ x11 . λ x12 : ι → ι . x9 0)) x6 (x3 (λ x9 . x1 (λ x10 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι → ι . 0) (λ x10 : ι → ι . λ x11 . λ x12 : ι → ι . 0)) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x11 0)) (setsum (x5 (λ x9 x10 x11 . 0) 0) (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0)))))) ⟶ False (proof)
Theorem 269d3.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (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 . (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 : (ι → ι) → ι . Inj0 0) (x6 (setsum 0 0) (λ x9 . 0) (x4 0)) = x6 (Inj0 (Inj0 (Inj1 (Inj1 0)))) (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x3 (λ x14 : (ι → ι) → ι . x2 (λ x15 . λ x16 : ((ι → ι) → ι → ι) → ι . λ x17 : ι → ι . λ x18 x19 . 0) 0) (x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 x18 . 0) 0)) (setsum 0 0))) x7) ⟶ (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 x7 . x3 (λ x9 : (ι → ι) → ι . Inj0 0) (x3 (λ x9 : (ι → ι) → ι . 0) (x1 (λ x9 . λ x10 : (ι → ι) → ι . x6) x7)) = x3 (λ x9 : (ι → ι) → ι . x5 0 (λ x10 . x1 (λ x11 . λ x12 : (ι → ι) → ι . x3 (λ x13 : (ι → ι) → ι . 0) (x1 (λ x13 . λ x14 : (ι → ι) → ι . 0) 0)) (Inj0 0)) 0) (Inj0 (x3 (λ x9 : (ι → ι) → ι . x0 (λ x10 . x9 (λ x11 . 0)) x7) x6))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . Inj0 (x2 (λ x14 . λ x15 : ((ι → ι) → ι → ι) → ι . λ x16 : ι → ι . λ x17 x18 . 0) 0)) (setsum (setsum (Inj1 0) (Inj1 (x1 (λ x9 . λ x10 : (ι → ι) → ι . 0) 0))) 0) = Inj0 0) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι . ∀ x7 . x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x1 (λ x14 . λ x15 : (ι → ι) → ι . x3 (λ x16 : (ι → ι) → ι . x3 (λ x17 : (ι → ι) → ι . 0) (Inj0 0)) (setsum 0 0)) (Inj0 x13)) (x0 (λ x9 . Inj1 (setsum (x3 (λ x10 : (ι → ι) → ι . 0) 0) (x3 (λ x10 : (ι → ι) → ι . 0) 0))) (setsum (setsum (x1 (λ x9 . λ x10 : (ι → ι) → ι . 0) 0) 0) (Inj1 (x3 (λ x9 : (ι → ι) → ι . 0) 0)))) = setsum (setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . x13) (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . setsum 0 0) x7)) 0) (setsum (x1 (λ x9 . λ x10 : (ι → ι) → ι . 0) x7) (x3 (λ x9 : (ι → ι) → ι . x0 (λ x10 . x7) (x1 (λ x10 . λ x11 : (ι → ι) → ι . 0) 0)) (x4 (x3 (λ x9 : (ι → ι) → ι . 0) 0) (λ x9 . setsum 0 0) (x6 (λ x9 . λ x10 : ι → ι . 0) 0) (x6 (λ x9 . λ x10 : ι → ι . 0) 0))))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : (ι → ι) → ι . x1 (λ x11 . λ x12 : (ι → ι) → ι . setsum x11 0) (x10 (λ x11 . 0))) (x4 (λ x9 . λ x10 : ι → ι . setsum (Inj1 (x3 (λ x11 : (ι → ι) → ι . 0) 0)) (x1 (λ x11 . λ x12 : (ι → ι) → ι . x10 0) (x1 (λ x11 . λ x12 : (ι → ι) → ι . 0) 0))) 0) = setsum (setsum 0 (x4 (λ x9 . λ x10 : ι → ι . x6 0 (x6 0 0 0) (x1 (λ x11 . λ x12 : (ι → ι) → ι . 0) 0)) (x1 (λ x9 . λ x10 : (ι → ι) → ι . Inj0 0) (setsum 0 0)))) (x7 (setsum (x4 (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : (ι → ι) → ι . 0) 0) (x7 0)) (setsum (setsum 0 0) (x7 0))))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x6 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 . λ x10 : (ι → ι) → ι . x3 (λ x11 : (ι → ι) → ι . x3 (λ x12 : (ι → ι) → ι . 0) (setsum (Inj0 0) (x10 (λ x12 . 0)))) 0) (x3 (λ x9 : (ι → ι) → ι . x0 (λ x10 . x10) (x3 (λ x10 : (ι → ι) → ι . 0) (Inj0 0))) (Inj1 (setsum (x1 (λ x9 . λ x10 : (ι → ι) → ι . 0) 0) x7))) = Inj1 0) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι → ι . x0 (λ x9 . 0) 0 = x4 (λ x9 x10 . x7 0 (Inj0 0))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . x0 (λ x10 . x1 (λ x11 . λ x12 : (ι → ι) → ι . 0) x9) x9) (setsum 0 (x1 (λ x9 . λ x10 : (ι → ι) → ι . x0 (λ x11 . x1 (λ x12 . λ x13 : (ι → ι) → ι . 0) 0) (x2 (λ x11 . λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 : ι → ι . λ x14 x15 . 0) 0)) (x0 (λ x9 . 0) 0))) = setsum (x2 (λ x9 . λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 : ι → ι . λ x12 x13 . 0) 0) 0) ⟶ False (proof)
Theorem aa86e.. : ∀ x0 : (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 → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x2 : ((((ι → ι) → ι) → ι) → ι → ι → ι) → ι → ι . ∀ x3 : (ι → ι → ι → (ι → ι) → ι) → ι → ι . (∀ x4 : ι → (ι → ι → ι) → ι → ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 x11 . λ x12 : ι → ι . 0) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x3 (λ x9 x10 x11 . λ x12 : ι → ι . x2 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . Inj0 (Inj0 (setsum 0 0))) (x12 (x2 (λ x13 : ((ι → ι) → ι) → ι . λ x14 x15 . x2 (λ x16 : ((ι → ι) → ι) → ι . λ x17 x18 . 0) 0) 0))) (x3 (λ x9 x10 x11 . λ x12 : ι → ι . x0 (λ x13 x14 . x1 (λ x15 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 : (ι → ι) → ι → ι . x14) (λ x15 . 0)) (λ x13 : ι → ι → ι → ι . λ x14 . 0) (Inj0 (Inj0 0))) (x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x3 (λ x12 x13 x14 . λ x15 : ι → ι . 0) (Inj1 0)) (setsum (setsum 0 0) (setsum 0 0)))) = Inj1 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x0 (λ x12 x13 . x11) (λ x12 : ι → ι → ι → ι . λ x13 . x2 (λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . Inj1 0) x11) (x0 (λ x12 x13 . x2 (λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . x15) 0) (λ x12 : ι → ι → ι → ι . λ x13 . Inj1 (x12 0 0 0)) 0)) x7 = setsum 0 (setsum (setsum x7 (Inj1 x5)) (x0 (λ x9 x10 . 0) (λ x9 : ι → ι → ι → ι . λ x10 . x10) 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ((ι → ι) → ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . 0) x7 = x7) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι → ι . ∀ x7 . x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι → ι . 0) (λ x9 . x2 (λ x10 : ((ι → ι) → ι) → ι . λ x11 x12 . 0) (x0 (λ x10 x11 . x9) (λ x10 : ι → ι → ι → ι . λ x11 . 0) (x3 (λ x10 x11 x12 . λ x13 : ι → ι . 0) x9))) = setsum (x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . setsum (Inj0 (setsum 0 0)) (x9 (λ x12 : ι → ι . 0))) 0) 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x9 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι → ι . setsum (Inj1 (x9 (λ x12 : ι → ι → ι . λ x13 : ι → ι . x2 (λ x14 : ((ι → ι) → ι) → ι . λ x15 x16 . 0) 0))) 0) (λ x9 . x9) = x4 (λ x9 x10 : ι → ι . x0 (λ x11 . x2 (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . x14)) (λ x11 : ι → ι → ι → ι . λ x12 . x0 (λ x13 x14 . x2 (λ x15 : ((ι → ι) → ι) → ι . λ x16 x17 . Inj0 0) (Inj1 0)) (λ x13 : ι → ι → ι → ι . λ x14 . x0 (λ x15 x16 . x15) (λ x15 : ι → ι → ι → ι . λ x16 . setsum 0 0) (x0 (λ x15 x16 . 0) (λ x15 : ι → ι → ι → ι . λ x16 . 0) 0)) 0) (Inj0 0)) (λ x9 . x3 (λ x10 x11 x12 . λ x13 : ι → ι . 0) x6) (x7 (λ x9 . x6) (λ x9 : ι → ι . λ x10 . Inj0 (Inj1 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . x0 (λ x9 x10 . x2 (λ x11 : ((ι → ι) → ι) → ι . λ x12 x13 . 0) (x1 (λ x11 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι → ι . 0) (λ x11 . x3 (λ x12 x13 x14 . λ x15 : ι → ι . x14) (setsum 0 0)))) (λ x9 : ι → ι → ι → ι . λ x10 . Inj1 (x3 (λ x11 x12 x13 . λ x14 : ι → ι . setsum (Inj1 0) 0) 0)) (x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x2 (λ x12 : ((ι → ι) → ι) → ι . λ x13 x14 . 0) 0) (Inj1 (Inj1 (x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (λ x9 x10 . 0) 0 0)))) = x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . Inj1 (setsum 0 0)) (setsum (x2 (λ x9 : ((ι → ι) → ι) → ι . λ x10 x11 . x7 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0) (λ x12 x13 . x13) (x1 (λ x12 : ((ι → ι → ι) → (ι → ι) → ι) → ι . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : (ι → ι) → ι → ι . 0) (λ x12 . 0)) x10) 0) 0)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x9 x10 . 0) (λ x9 : ι → ι → ι → ι . λ x10 . Inj1 0) 0 = x5) ⟶ False (proof)
Theorem 813f2.. : ∀ x0 : (ι → ι) → (ι → ι → ι) → ι . ∀ x1 : (((((ι → ι) → ι → ι) → (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 . ∀ x3 : (((((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 . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → ι → (ι → ι) → ι . x3 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . 0) (Inj1 (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . x3 (λ x11 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 x15 . 0) (x10 (λ x11 . 0) (λ x11 . 0) 0)) (λ x9 : ι → ι . λ x10 . Inj1 (x2 (λ x11 : ι → ι . λ x12 . 0) 0 (λ x11 : ι → ι . λ x12 . 0))))) = setsum (Inj0 (Inj0 (x3 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . setsum 0 0) (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0))))) (Inj1 (x7 (x7 (Inj0 0) 0 (λ x9 . x6 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) 0)) 0 (λ x9 . setsum (Inj0 0) (setsum 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . x13) (setsum (x0 (λ x9 . x2 (λ x10 : ι → ι . λ x11 . 0) (Inj1 0) (λ x10 : ι → ι . λ x11 . setsum 0 0)) (λ x9 x10 . x9)) (x2 (λ x9 : ι → ι . λ x10 . Inj1 (x0 (λ x11 . 0) (λ x11 x12 . 0))) (setsum (x6 0) (x0 (λ x9 . 0) (λ x9 x10 . 0))) (λ x9 : ι → ι . λ x10 . setsum (Inj0 0) 0))) = x7) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → ι . λ x10 . setsum (x2 (λ x11 : ι → ι . λ x12 . setsum 0 0) (Inj0 (x9 0)) (λ x11 : ι → ι . λ x12 . Inj0 (Inj0 0))) x7) x7 (λ x9 : ι → ι . λ x10 . x0 (λ x11 . setsum (x3 (λ x12 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 x16 . x2 (λ x17 : ι → ι . λ x18 . 0) 0 (λ x17 : ι → ι . λ x18 . 0)) (Inj0 0)) 0) (λ x11 x12 . x9 (x1 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x14 : (ι → ι) → (ι → ι) → ι → ι . x13 (λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0)) (λ x13 : ι → ι . λ x14 . Inj1 0)))) = x0 (λ x9 . Inj1 0) (λ x9 x10 . setsum 0 x9)) ⟶ (∀ x4 . ∀ x5 x6 : ι → ι . ∀ x7 : ((ι → ι) → ι → ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 . x0 (λ x11 . x7 (λ x12 : ι → ι . λ x13 x14 . setsum x14 (x3 (λ x15 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 x19 . 0) 0))) (λ x11 x12 . 0)) 0 (λ x9 : ι → ι . λ x10 . setsum (x0 (λ x11 . x0 (λ x12 . x12) (λ x12 x13 . setsum 0 0)) (λ x11 x12 . setsum (setsum 0 0) (setsum 0 0))) (setsum 0 x10)) = Inj0 (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . Inj1 (x6 (setsum 0 0))) (λ x9 : ι → ι . λ x10 . x9 0))) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . x0 (λ x11 . 0) (λ x11 x12 . 0)) (λ x9 : ι → ι . λ x10 . x7) = setsum 0 (x3 (λ x9 : (((ι → ι) → ι) → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 . λ x11 : ι → ι . λ x12 x13 . x11 (x2 (λ x14 : ι → ι . λ x15 . 0) (Inj1 0) (λ x14 : ι → ι . λ x15 . 0))) x7)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ι → ι . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι → ι) → ((ι → ι) → ι → ι) → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . 0) (λ x9 : ι → ι . λ x10 . 0) = setsum 0 (setsum (x6 (λ x9 x10 x11 . x11) (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . x7 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . λ x12 . 0)) (λ x9 : ι → ι . λ x10 . 0))) (x0 (λ x9 . x9) (λ x9 x10 . setsum (x2 (λ x11 : ι → ι . λ x12 . 0) 0 (λ x11 : ι → ι . λ x12 . 0)) (x7 (λ x11 : (ι → ι) → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . λ x12 . 0)))))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (((ι → ι) → ι) → ι → ι → ι) → ι . ∀ x7 . x0 (λ x9 . x5 0) (λ x9 x10 . 0) = setsum 0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x0 (λ x9 . x2 (λ x10 : ι → ι . λ x11 . setsum 0 x9) (x0 (λ x10 . setsum (x7 (λ x11 x12 x13 . 0)) (setsum 0 0)) (λ x10 x11 . x10)) (λ x10 : ι → ι . λ x11 . x7 (λ x12 x13 x14 . x2 (λ x15 : ι → ι . λ x16 . x14) (Inj1 0) (λ x15 : ι → ι . λ x16 . x16)))) (λ x9 x10 . x7 (λ x11 x12 x13 . x0 (λ x14 . 0) (λ x14 x15 . Inj0 (x0 (λ x16 . 0) (λ x16 x17 . 0))))) = Inj1 (x0 (λ x9 . 0) (λ x9 x10 . 0))) ⟶ False (proof)
Theorem f3264.. : ∀ 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 . ∀ x2 : (((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 . ∀ x3 : (ι → ι → ((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . (∀ x4 : (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x0 (λ x13 . setsum (setsum 0 x13) 0) (λ x13 . 0) (λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) (x11 (λ x13 . x12 (x12 0))) (Inj1 (x3 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0) (x3 (λ x13 x14 . λ x15 : (ι → ι) → ι . λ x16 : ι → ι . 0) 0)))) 0 = x0 (λ x9 . setsum x9 (x0 (λ x10 . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . x2 (λ x15 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → ι . λ x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 x16 . 0)) x9) (λ x10 . x10) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 (setsum 0 0)) x6 x9)) (λ x9 . setsum (x0 (λ x10 . 0) (λ x10 . x10) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . x9) (Inj0 0) (setsum (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0) 0) (x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0) 0))) x9) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . x14 (λ x15 . Inj1 0) 0) (Inj0 0) (λ x12 x13 . Inj0 (Inj1 0))) (x10 (x10 0))) (x0 (λ x9 . x9) (λ x9 . x2 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . x12 (λ x13 . 0) 0) (setsum (x1 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . 0) (λ x10 . 0)) (x0 (λ x10 . 0) (λ x10 . 0) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0)) (λ x10 x11 . x9)) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . x12 (λ x15 x16 x17 . x2 (λ x18 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x19 : (ι → ι → ι) → ι . λ x20 : (ι → ι) → ι → ι . 0) 0 (λ x18 x19 . 0)) (λ x15 : ι → ι . Inj1 0) (λ x15 . Inj1 0) (setsum 0 0)) (x0 (λ x12 . setsum 0 0) (λ x12 . x12) (λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 0) (x10 0) 0) (λ x12 x13 . x13)) (x7 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . setsum 0 0) 0)) x6) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x2 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . x2 (λ x16 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → ι . λ x18 : (ι → ι) → ι → ι . 0) (x0 (λ x16 . 0) (λ x16 . 0) (λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0 0) (λ x16 x17 . x1 (λ x18 . 0) 0 (λ x18 : ι → ι → ι . 0) (λ x18 . 0))) (x12 (x1 (λ x13 . 0) 0 (λ x13 : ι → ι → ι . 0) (λ x13 . 0))) (λ x13 x14 . x1 (λ x15 . x13) (x2 (λ x15 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 : (ι → ι → ι) → ι . λ x17 : (ι → ι) → ι → ι . 0) 0 (λ x15 x16 . 0)) (λ x15 : ι → ι → ι . 0) (λ x15 . 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x2 (λ x13 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 : (ι → ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . 0) 0 (λ x13 x14 . x11 (λ x15 . x13))) (setsum (x0 (λ x9 . 0) (λ x9 . x5) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x7) 0 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) x6)) (x0 (λ x9 . 0) (λ x9 . x5) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 : (ι → ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . 0) 0 (λ x12 x13 . 0)) (x9 (λ x12 . 0) 0)) (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x9) (Inj1 0)) x5)) = Inj1 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . x10) x7)) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 . ∀ x6 : ι → (ι → ι) → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . Inj0 0) (Inj1 (Inj0 0)) (λ x9 x10 . Inj1 x9) = x4 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . setsum (x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . x2 (λ x16 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 : (ι → ι → ι) → ι . λ x18 : (ι → ι) → ι → ι . setsum 0 0) (x1 (λ x16 . 0) 0 (λ x16 : ι → ι → ι . 0) (λ x16 . 0)) (λ x16 x17 . x0 (λ x18 . 0) (λ x18 . 0) (λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0) 0 0)) 0) (setsum (x1 (λ x12 . Inj1 0) (Inj0 0) (λ x12 : ι → ι → ι . x9 (λ x13 . 0) 0) (λ x12 . setsum 0 0)) x7))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : ι → ι . ∀ x7 : (ι → ι → ι → ι) → ι . x2 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . Inj1 0) (setsum (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (Inj1 (x0 (λ x9 . 0) (λ x9 . 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 0))) 0) (λ x9 x10 . x9) = setsum x4 0) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 . Inj1 0) x6 (λ x9 : ι → ι → ι . 0) (λ x9 . 0) = x6) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι → ι → ι → ι . x1 (λ x9 . Inj1 (setsum 0 (x5 (Inj1 0) (x1 (λ x10 . 0) 0 (λ x10 : ι → ι → ι . 0) (λ x10 . 0))))) 0 (λ x9 : ι → ι → ι . setsum (x9 (x5 (Inj0 0) (x2 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . 0) 0 (λ x10 x11 . 0))) 0) (Inj0 0)) (λ x9 . setsum x6 (x5 (x1 (λ x10 . x0 (λ x11 . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0) 0 (λ x10 : ι → ι → ι . Inj0 0) (λ x10 . x0 (λ x11 . 0) (λ x11 . 0) (λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0)) 0)) = Inj1 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) (x7 (x2 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . x10 (λ x12 x13 . 0)) x6 (λ x9 x10 . x3 (λ x11 x12 . λ x13 : (ι → ι) → ι . λ x14 : ι → ι . 0) 0)) 0 0 x4))) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 . x2 (λ x10 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 : (ι → ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . Inj0 (Inj1 (x1 (λ x13 . 0) 0 (λ x13 : ι → ι → ι . 0) (λ x13 . 0)))) x9 (λ x10 x11 . x9)) (λ x9 . Inj0 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . Inj1 0) (setsum x7 (setsum (Inj0 (x3 (λ x9 x10 . λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0)) 0)) (x1 (λ x9 . 0) x5 (λ x9 : ι → ι → ι . 0) (λ x9 . 0)) = x2 (λ x9 : (ι → ι → ι → ι) → ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x10 : (ι → ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . setsum 0 (Inj1 0)) x7 (λ x9 x10 . Inj1 0)) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι → ι . x0 (λ x9 . 0) (λ x9 . Inj0 x6) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 (x0 (λ x9 . 0) (λ x9 . setsum 0 0) (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . 0) (x4 (x1 (λ x9 . x6) 0 (λ x9 : ι → ι → ι . x3 (λ x10 x11 . λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0) 0) (λ x9 . x9))) (setsum x6 x6)) = Inj1 (x1 (λ x9 . x0 (λ x10 . x7 (λ x11 : ι → ι → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) (setsum 0 0)) (λ x10 . x9) (λ x10 : (ι → ι) → ι → ι . λ x11 : ι → ι . x3 (λ x12 x13 . λ x14 : (ι → ι) → ι . λ x15 : ι → ι . x13)) x6 x6) (x5 (setsum (x4 0) 0)) (λ x9 : ι → ι → ι . 0) (λ x9 . x6))) ⟶ False (proof)
Theorem 6b7c6.. : ∀ x0 : (((ι → ι) → ι) → ι → ι → (ι → ι) → ι) → ι → (((ι → ι) → ι) → ι) → ι . ∀ x1 : (ι → ι) → ι → ι → ι . ∀ x2 : (ι → ((ι → ι) → ι) → ((ι → ι) → ι → 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 → ι) → ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ι → ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : ι → (ι → ι) → ι . λ x10 . x1 (λ x11 . x9 0 (λ x12 . setsum 0 (x1 (λ x13 . 0) 0 0))) (x7 (x3 (λ x11 : ι → (ι → ι) → ι . λ x12 . x12) (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 . 0) 0 0))) (x3 (λ x11 : ι → (ι → ι) → ι . λ x12 . x0 (λ x13 : (ι → ι) → ι . λ x14 x15 . λ x16 : ι → ι . Inj0 0) (x2 (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . 0) (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) 0) (λ x13 : (ι → ι) → ι . x10)) (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : ι → ι . λ x14 . 0))) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) = setsum (x5 (x1 (λ x9 . x9) (Inj0 0) (x7 (x1 (λ x9 . 0) 0 0))) (setsum (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → (ι → ι) → ι . λ x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x9 (λ x12 . 0)) 0) (x5 0 0 0 (x7 0))) (Inj1 (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x1 (λ x13 . 0) 0 0) x4 (λ x9 : (ι → ι) → ι . setsum 0 0))) (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x12 (x3 (λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0))) x4 (λ x9 : (ι → ι) → ι . x7 (x3 (λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 : ι → (ι → ι) → ι . λ x10 . setsum (x7 (λ x11 . x9 x10 (λ x12 . Inj0 0))) (setsum (x1 (λ x11 . 0) (Inj1 0) 0) 0)) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . Inj1) = setsum (x1 (λ x9 . x7 (λ x10 . Inj0 0)) (x6 0 (x4 0)) (x7 (λ x9 . x3 (λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0)))) (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x10) (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . Inj0 (x3 (λ x13 : ι → (ι → ι) → ι . λ x14 . 0) (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . 0))) (x7 (λ x9 . x7 (λ x10 . 0))) (λ x9 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . x0 (λ x10 : (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . setsum (x0 (λ x14 : (ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . 0) 0 (λ x14 : (ι → ι) → ι . 0)) (x13 0)) 0 (λ x10 : (ι → ι) → ι . x10 (λ x11 . x0 (λ x12 : (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι → ι → ι . x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x10) (setsum (Inj1 (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι) → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (x4 0))) 0) = x5 (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . 0) 0) (setsum (Inj0 0) (Inj0 (Inj1 (x7 0 (λ x9 : ι → ι . 0) 0 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : (ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . x14 (λ x18 . 0)) (x1 (λ x14 . 0) x13 0) (λ x14 : (ι → ι) → ι . setsum (setsum (setsum 0 0) (x11 (λ x15 . 0) 0)) 0)) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x11 (x11 (x11 0))) (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 (x11 (λ x14 . x11 (λ x15 . 0) 0) (x3 (λ x14 : ι → (ι → ι) → ι . λ x15 . 0) (λ x14 : (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0)))) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x2 (λ x12 . λ x13 : (ι → ι) → ι . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . Inj0 (x14 (λ x17 . 0) 0)) (λ x12 : (ι → ι) → ι . λ x13 . λ x14 : ι → ι . x1 (λ x15 . x2 (λ x16 . λ x17 : (ι → ι) → ι . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 : (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0) (x3 (λ x15 : ι → (ι → ι) → ι . λ x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0)) (x0 (λ x15 : (ι → ι) → ι . λ x16 x17 . λ x18 : ι → ι . 0) 0 (λ x15 : (ι → ι) → ι . 0))) (x1 (λ x12 . 0) (x1 (λ x12 . 0) 0 0) (x0 (λ x12 : (ι → ι) → ι . λ x13 x14 . λ x15 : ι → ι . 0) 0 (λ x12 : (ι → ι) → ι . 0)))) (x7 0 (λ x9 : ι → ι . x5))) = setsum (x6 (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x3 (λ x12 : ι → (ι → ι) → ι . λ x13 . setsum 0 0) (λ x12 : (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . x1 (λ x16 . 0) 0 0)) (x1 (λ x9 . x1 (λ x10 . 0) 0 0) (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . 0) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . 0) 0) (x4 0)))) 0) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → ι) → (ι → ι) → ι → ι . ∀ x6 : ι → ι . ∀ x7 . x1 (λ x9 . x9) (x1 (λ x9 . x9) (Inj0 (setsum (Inj1 0) (x1 (λ x9 . 0) 0 0))) x4) x7 = x7) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . setsum (x0 (λ x10 : (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x1 (λ x14 . x3 (λ x15 : ι → (ι → ι) → ι . λ x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0)) (setsum 0 0) 0) x9 (λ x10 : (ι → ι) → ι . 0)) 0) (x5 0 (x4 (λ x9 . 0) (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x0 (λ x14 : (ι → ι) → ι . λ x15 x16 . λ x17 : ι → ι . 0) 0 (λ x14 : (ι → ι) → ι . 0)) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . setsum 0 0) 0) (λ x9 . x2 (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x3 (λ x15 : ι → (ι → ι) → ι . λ x16 . 0) (λ x15 : (ι → ι) → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0)) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum 0 0) (Inj1 0)))) (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x2 (λ x13 . λ x14 : (ι → ι) → ι . λ x15 : (ι → ι) → ι → ι . λ x16 : ι → ι . λ x17 . Inj1 (x3 (λ x18 : ι → (ι → ι) → ι . λ x19 . 0) (λ x18 : (ι → ι) → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0))) (λ x13 : (ι → ι) → ι . λ x14 . λ x15 : ι → ι . x12 (x3 (λ x16 : ι → (ι → ι) → ι . λ x17 . 0) (λ x16 : (ι → ι) → ι . λ x17 . λ x18 : ι → ι . λ x19 . 0))) x11) x7 (λ x9 : (ι → ι) → ι . x1 (λ x10 . x0 (λ x11 : (ι → ι) → ι . λ x12 x13 . λ x14 : ι → ι . 0) (x2 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) 0) (λ x11 : (ι → ι) → ι . Inj1 0)) (x5 (x9 (λ x10 . 0)) (x6 0 0 (λ x10 . 0))) 0)) = setsum (Inj1 (x2 (λ x9 . λ x10 : (ι → ι) → ι . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x3 (λ x14 : ι → (ι → ι) → ι . λ x15 . x12 0) (λ x14 : (ι → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . x17)) (λ x9 : (ι → ι) → ι . λ x10 . λ x11 : ι → ι . x1 (λ x12 . 0) (x3 (λ x12 : ι → (ι → ι) → ι . λ x13 . 0) (λ x12 : (ι → ι) → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0)) (setsum 0 0)) 0)) (Inj1 (x5 x7 (Inj0 0)))) ⟶ (∀ x4 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι) → (ι → ι) → (ι → ι) → ι . x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x10) (x1 (λ x9 . x0 (λ x10 : (ι → ι) → ι . λ x11 x12 . λ x13 : ι → ι . x11) (x7 (λ x10 : ι → ι → ι . x7 (λ x11 : ι → ι → ι . 0) (λ x11 . 0) (λ x11 . 0)) (λ x10 . x2 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) 0) (λ x10 . x1 (λ x11 . 0) 0 0)) (λ x10 : (ι → ι) → ι . setsum x9 (setsum 0 0))) (setsum (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x10) (Inj0 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : ι → (ι → ι) → ι . λ x11 . 0) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) (x4 (λ x9 . Inj0 0) (setsum 0 0) (λ x9 . x9) (x7 (λ x9 : ι → ι → ι . 0) (λ x9 . 0) (λ x9 . 0)))) 0) (λ x9 : (ι → ι) → ι . Inj1 x6) = x1 (λ x9 . x1 (λ x10 . x1 (λ x11 . 0) (x2 (λ x11 . λ x12 : (ι → ι) → ι . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . x2 (λ x16 . λ x17 : (ι → ι) → ι . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 : (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0) (λ x11 : (ι → ι) → ι . λ x12 . λ x13 : ι → ι . Inj1 0) 0) 0) (x5 0 (λ x10 : ι → ι . λ x11 . 0)) 0) (x1 (λ x9 . 0) (x7 (λ x9 : ι → ι → ι . 0) (λ x9 . 0) (λ x9 . setsum 0 0)) (Inj1 (Inj0 (x4 (λ x9 . 0) 0 (λ x9 . 0) 0)))) x6) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 x7 . x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . 0) (x1 (λ x9 . 0) x7 (x4 (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x10) 0 (λ x9 : (ι → ι) → ι . x2 (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) 0)))) (λ x9 : (ι → ι) → ι . 0) = x1 (λ x9 . x2 (λ x10 . λ x11 : (ι → ι) → ι . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . Inj1 (x12 (λ x15 . x2 (λ x16 . λ x17 : (ι → ι) → ι . λ x18 : (ι → ι) → ι → ι . λ x19 : ι → ι . λ x20 . 0) (λ x16 : (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0) (setsum 0 0))) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (x3 (λ x10 : ι → (ι → ι) → ι . λ x11 . x9) (λ x10 : (ι → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0))) (Inj0 (x0 (λ x9 : (ι → ι) → ι . λ x10 x11 . λ x12 : ι → ι . x11) x7 (λ x9 : (ι → ι) → ι . x9 (λ x10 . 0)))) (setsum (setsum (Inj0 0) (setsum x6 0)) 0)) ⟶ False (proof)
Theorem c772a.. : ∀ x0 : (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 . ∀ x2 : ((ι → (ι → ι → 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 → ι) → ι → ι) → ι → (((ι → ι) → ι) → (ι → ι) → ι) → ι → ι . (∀ x4 : (ι → ι → ι) → ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι → ι → ι . ∀ x7 : ((ι → ι → ι) → (ι → ι) → ι) → ι → ι → ι . x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (x4 (λ x9 x10 . Inj1 0) (Inj1 (setsum (x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . 0) 0 0) 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x2 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : (ι → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . 0) (x3 (λ x12 : ι → ι → ι → ι → ι . λ x13 : ι → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x3 (λ x17 : ι → ι → ι → ι → ι . λ x18 : ι → ι → ι → ι . λ x19 . λ x20 : ι → ι . λ x21 . 0) 0 (λ x17 : (ι → ι) → ι . λ x18 : ι → ι . 0) 0) x9 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . x11 (λ x14 . 0) 0) (setsum 0 0))) (Inj0 0)) = setsum (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (x4 (λ x9 x10 . 0) 0)) x5) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x12 (x0 (λ x14 x15 . λ x16 : (ι → ι) → ι . x2 (λ x17 : ι → (ι → ι → ι) → ι . λ x18 : (ι → ι) → (ι → ι) → ι → ι . λ x19 x20 x21 . setsum 0 0) 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . setsum (x14 (λ x18 . 0)) (Inj0 0)) 0)) (Inj1 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum x6 (setsum 0 (x0 (λ x11 x12 . λ x13 : (ι → ι) → ι . x2 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 : (ι → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . 0) 0) (λ x11 : (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x12 0 0) (x3 (λ x11 : ι → ι → ι → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0)))) (x7 (λ x9 : (ι → ι) → ι . x9 (λ x10 . x9 (λ x11 . 0)))) = x7 (λ x9 : (ι → ι) → ι . setsum 0 (x3 (λ x10 : ι → ι → ι → ι → ι . λ x11 : ι → ι → ι → ι . λ x12 . λ x13 : ι → ι . λ x14 . x13 (x11 0 0 0)) 0 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x14 (λ x15 . 0) 0) (x10 (λ x12 . 0))) (x5 x6 (λ x10 . x6))))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . setsum (x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . setsum (x16 (λ x17 . 0) 0) (Inj1 0)) (Inj0 (x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0))) (x1 (λ x14 x15 . λ x16 : (ι → ι) → ι → ι . x14) 0)) (setsum (setsum (Inj0 0) 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . setsum 0 0) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . Inj0 0) 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x9 (λ x13 . x10 0 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . setsum 0 0) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . 0) 0)))) = x6) ⟶ (∀ x4 x5 x6 x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x0 (λ x14 x15 . λ x16 : (ι → ι) → ι . x14) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . 0) (Inj1 (x2 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 : (ι → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . x16) x13))) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x2 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 : (ι → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . x1 (λ x19 x20 . λ x21 : (ι → ι) → ι → ι . x0 (λ x22 x23 . λ x24 : (ι → ι) → ι . 0) (λ x22 : (ι → ι) → ι . λ x23 : ι → ι → ι . λ x24 : ι → ι . λ x25 . 0) 0) (x1 (λ x19 x20 . λ x21 : (ι → ι) → ι → ι . 0) 0)) (setsum (x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) 0)) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 : (ι → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . x0 (λ x19 x20 . λ x21 : (ι → ι) → ι . 0) (λ x19 : (ι → ι) → ι . λ x20 : ι → ι → ι . λ x21 : ι → ι . λ x22 . 0) 0) (x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) (setsum 0 0)) (Inj0 (setsum 0 0)))) = Inj0 (setsum x6 (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) 0))) ⟶ (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) 0 = Inj1 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (Inj1 x10)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj1 (x10 0 (x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) 0))) x4)) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → (ι → ι) → ι → ι . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι . x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . x3 (λ x12 : ι → ι → ι → ι → ι . λ x13 : ι → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x0 (λ x17 x18 . λ x19 : (ι → ι) → ι . Inj0 (setsum 0 0)) (λ x17 : (ι → ι) → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . Inj0 (setsum 0 0)) (x15 (setsum 0 0))) (x2 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : (ι → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . setsum (setsum 0 0) x14) (setsum (x11 (λ x12 . 0) 0) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) 0))) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . setsum 0 (Inj0 (setsum 0 0))) 0) (x6 (Inj0 (x4 (λ x9 . 0))) (setsum 0 0) (λ x9 . x5) (x6 (x4 (λ x9 . setsum 0 0)) (x7 (λ x9 : ι → ι → ι . λ x10 . x6 0 0 (λ x11 . 0) 0)) (λ x9 . setsum (setsum 0 0) 0) (Inj0 0))) = x6 (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x0 (λ x12 x13 . λ x14 : (ι → ι) → ι . Inj0 (x0 (λ x15 x16 . λ x17 : (ι → ι) → ι . 0) (λ x15 : (ι → ι) → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0)) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x13 0 (Inj0 0)) (Inj1 (Inj0 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0)) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x2 (λ x12 : ι → (ι → ι → ι) → ι . λ x13 : (ι → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . x15) (x3 (λ x12 : ι → ι → ι → ι → ι . λ x13 : ι → ι → ι → ι . λ x14 . λ x15 : ι → ι . λ x16 . x13 0 0 0) (x11 (λ x12 . 0)) (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . 0) (Inj1 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . setsum 0 (Inj1 0)) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x16) (x1 (λ x13 x14 . λ x15 : (ι → ι) → ι → ι . 0) (x9 (λ x13 . 0)))) (x4 (λ x9 . x6 (x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 : (ι → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) 0) 0 (λ x10 . x3 (λ x11 : ι → ι → ι → ι → ι . λ x12 : ι → ι → ι → ι . λ x13 . λ x14 : ι → ι . λ x15 . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . 0) 0) 0))) (λ x9 . Inj0 (Inj0 0)) (x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x7 (λ x12 : ι → ι → ι . λ x13 . setsum (x3 (λ x14 : ι → ι → ι → ι → ι . λ x15 : ι → ι → ι → ι . λ x16 . λ x17 : ι → ι . λ x18 . 0) 0 (λ x14 : (ι → ι) → ι . λ x15 : ι → ι . 0) 0) (setsum 0 0))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . setsum (x3 (λ x13 : ι → ι → ι → ι → ι . λ x14 : ι → ι → ι → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) (Inj0 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι . Inj1 0) (Inj1 0)) (setsum (Inj0 0) (x11 0))) (x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (x3 (λ x9 : ι → ι → ι → ι → ι . λ x10 : ι → ι → ι → ι . λ x11 . λ x12 : ι → ι . λ x13 . x13) (x4 (λ x9 . 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . setsum 0 0) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0) (Inj1 (x4 (λ x9 . 0)))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : ι → ι → (ι → ι) → ι . ∀ x7 . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x11 (λ x12 . x2 (λ x13 : ι → (ι → ι → ι) → ι . λ x14 : (ι → ι) → (ι → ι) → ι → ι . λ x15 x16 . setsum 0) (Inj0 x10))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (Inj1 (setsum 0 (x5 (setsum 0 0)))) = x5 0) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 x10 . λ x11 : (ι → ι) → ι . x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . x12) (x1 (λ x12 x13 . λ x14 : (ι → ι) → ι → ι . 0) (x11 (λ x12 . x9)))) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . setsum 0 (setsum (Inj0 (setsum 0 0)) (x0 (λ x13 x14 . λ x15 : (ι → ι) → ι . Inj0 0) (λ x13 : (ι → ι) → ι . λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) (Inj0 0)))) (x1 (λ x9 x10 . λ x11 : (ι → ι) → ι → ι . 0) (Inj1 (x6 x4))) = setsum x7 0) ⟶ False (proof)
Theorem b4427.. : ∀ x0 : ((((ι → ι) → ι) → ι) → ι) → ι → (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x1 x2 : (ι → ι) → ι → ι . ∀ x3 : (ι → (ι → (ι → ι) → ι → ι) → ι) → ι → ι → ((ι → ι) → ι) → (ι → ι) → ι → ι . (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x6 (x0 (λ x11 : ((ι → ι) → ι) → ι . Inj1 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . Inj0 (setsum 0 0)) 0)) (Inj0 0) (x1 (λ x9 . x2 (λ x10 . Inj0 0) (x3 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . x2 (λ x12 . 0) 0) (x1 (λ x10 . 0) 0) x9 (λ x10 : ι → ι . 0) (λ x10 . Inj1 0) (x2 (λ x10 . 0) 0))) x5) (λ x9 : ι → ι . Inj0 x5) (λ x9 . Inj0 (Inj0 (x2 (λ x10 . Inj1 0) 0))) (setsum x5 x7) = setsum (Inj1 (x6 (Inj0 (setsum 0 0)))) x7) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . setsum (x3 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . x3 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . 0) 0 x9 (λ x13 : ι → ι . x10 0 (λ x14 . 0) 0) (λ x13 . x12 0 (λ x14 . 0) 0) x11) (x2 (λ x11 . x3 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x12 : ι → ι . 0) (λ x12 . 0) 0) (x3 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x11 : ι → ι . 0) (λ x11 . 0) 0)) x6 (λ x11 : ι → ι . x0 (λ x12 : ((ι → ι) → ι) → ι . x9) 0 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . x11 0) (Inj1 0)) (λ x11 . x11) (setsum (x1 (λ x11 . 0) 0) (x0 (λ x11 : ((ι → ι) → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) 0))) 0) x7 x4 (λ x9 : ι → ι . Inj0 0) (λ x9 . x1 (λ x10 . x6) (x3 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . setsum x9 0) (x0 (λ x10 : ((ι → ι) → ι) → ι . 0) (x2 (λ x10 . 0) 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x13 : ι → ι . 0) (λ x13 . 0) 0) (x2 (λ x10 . 0) 0)) (x5 (λ x10 . x0 (λ x11 : ((ι → ι) → ι) → ι . 0) 0 (λ x11 : (ι → ι) → ι . λ x12 : ι → ι . λ x13 . 0) 0)) (λ x10 : ι → ι . 0) (λ x10 . 0) x7)) 0 = x1 (λ x9 . x9) (x1 (λ x9 . x9) (setsum (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . Inj0 0) x6 0 (λ x9 : ι → ι . Inj1 0) (λ x9 . x1 (λ x10 . 0) 0) 0) x7))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x5) 0 = setsum (x0 (λ x9 : ((ι → ι) → ι) → ι . x6 0) (Inj1 (x4 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . 0) (x0 (λ x9 : ((ι → ι) → ι) → ι . x6 0) (setsum 0 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x9 (λ x12 . 0)) 0) (Inj1 (Inj0 0)) (λ x9 : ι → ι . Inj0 (Inj0 0)) (λ x9 . 0) (setsum x5 x5))) (setsum (x1 (λ x9 . setsum (x1 (λ x10 . 0) 0) 0) (Inj1 x7)) (x0 (λ x9 : ((ι → ι) → ι) → ι . 0) x5 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum x7 (setsum 0 0)) (x2 (λ x9 . x2 (λ x10 . 0) 0) 0)))) ⟶ (∀ x4 : (ι → ι → ι) → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x9 . 0) (Inj0 0) = x5) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (ι → ι) → ι → (ι → ι) → ι → ι . x1 (λ x9 . Inj0 (Inj1 0)) (x2 (λ x9 . x5) (x0 (λ x9 : ((ι → ι) → ι) → ι . 0) (x2 (λ x9 . setsum 0 0) (Inj0 0)) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . x7 (λ x12 . setsum 0 0) 0 (λ x12 . x3 (λ x13 . λ x14 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x13 : ι → ι . 0) (λ x13 . 0) 0) (x1 (λ x12 . 0) 0)) (x2 (λ x9 . Inj0 0) 0))) = x2 (λ x9 . x7 (λ x10 . x2 (λ x11 . x7 (λ x12 . x2 (λ x13 . 0) 0) (x2 (λ x12 . 0) 0) (λ x12 . 0) (x0 (λ x12 : ((ι → ι) → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) 0)) x9) (x2 (λ x10 . setsum (setsum 0 0) (x7 (λ x11 . 0) 0 (λ x11 . 0) 0)) x6) (λ x10 . x10) (Inj1 (Inj1 0))) x5) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) (setsum (x4 0) x7) = x6 (λ x9 . x6 (λ x10 . x10))) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ((ι → ι) → ι) → ι . 0) x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum (x2 (λ x12 . Inj1 (Inj0 0)) x7) x7) 0 = x6) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι → ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (ι → (ι → ι) → ι) → ((ι → ι) → ι) → ι . x0 (λ x9 : ((ι → ι) → ι) → ι . x2 (λ x10 . 0) x6) (Inj1 0) (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . setsum (x10 0) 0) (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x2 (λ x11 . setsum (x2 (λ x12 . 0) 0) (x0 (λ x12 : ((ι → ι) → ι) → ι . 0) 0 (λ x12 : (ι → ι) → ι . λ x13 : ι → ι . λ x14 . 0) 0)) (x7 (λ x11 . λ x12 : ι → ι . x12 0) (λ x11 : ι → ι . 0))) (x5 (Inj0 (x5 0 0)) 0) (x3 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x6) (Inj1 (Inj1 0)) (x0 (λ x9 : ((ι → ι) → ι) → ι . x1 (λ x10 . 0) 0) x6 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) (x5 0 0)) (λ x9 : ι → ι . x9 (x1 (λ x10 . 0) 0)) (λ x9 . x5 (x7 (λ x10 . λ x11 : ι → ι . 0) (λ x10 : ι → ι . 0)) 0) 0) (λ x9 : ι → ι . x9 (x0 (λ x10 : ((ι → ι) → ι) → ι . Inj1 0) (x9 0) (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . λ x12 . 0) (x3 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x10 : ι → ι . 0) (λ x10 . 0) 0))) (λ x9 . 0) (x4 (Inj0 (x0 (λ x9 : ((ι → ι) → ι) → ι . 0) 0 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . λ x11 . 0) 0)) (λ x9 : ι → ι . x2 (λ x10 . x3 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . 0) 0 0 (λ x11 : ι → ι . 0) (λ x11 . 0) 0) x6) (x2 (λ x9 . 0) (Inj0 0)) (Inj0 (x1 (λ x9 . 0) 0)))) = Inj0 0) ⟶ False (proof)
Theorem 7c1fe.. : ∀ x0 : (((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 → 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) → ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ((ι → ι → ι) → ι) → (ι → ι) → ι . (∀ x4 x5 x6 x7 . x3 (λ x9 . 0) 0 (λ x9 : ι → ι → ι . Inj0 (Inj0 (Inj1 0))) (λ x9 . x9) = x6) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x3 (λ x9 . Inj1 (Inj0 0)) (x7 (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . Inj0 (Inj1 0)) (λ x9 . setsum (Inj1 0) (setsum 0 0)) (λ x9 : ι → ι → ι . λ x10 x11 . setsum (Inj0 0) 0) (λ x9 : ι → ι . 0) 0 (x4 (λ x9 : ι → ι → ι . x7 0)))) (λ x9 : ι → ι → ι . 0) (λ x9 . 0) = Inj1 (x7 (Inj0 (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . x9 (λ x12 . λ x13 : ι → ι . λ x14 . 0) (λ x12 x13 . 0) 0 0) (λ x9 . 0))))) ⟶ (∀ x4 : ι → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι → ι) → ι → ι) → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x11 (λ x14 . 0) (x2 (λ x14 : ((ι → ι) → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . 0) (x0 (λ x14 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 x16 . x13) (λ x14 . x1 (λ x15 : (ι → (ι → ι) → ι) → ι . λ x16 . λ x17 : (ι → ι) → ι . λ x18 x19 . 0) (λ x15 . 0) (λ x15 : ι → ι → ι . λ x16 x17 . 0) (λ x15 : ι → ι . 0) 0 0)))) (setsum 0 (x2 (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x13) (Inj0 0))) = x5) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . λ x13 . x10) 0 = x6 0) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ((ι → ι → ι) → ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 x11 . x10) (λ x9 : ι → ι . setsum (Inj1 (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . Inj0 0) (λ x10 . x2 (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0))) (setsum (x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x2 (λ x15 : ((ι → ι) → ι) → ι → ι → ι . λ x16 . λ x17 : (ι → ι) → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0) (setsum 0 0)) (x5 (Inj1 0)))) 0 (Inj0 (x2 (λ x9 : ((ι → ι) → ι) → ι → ι → ι . λ x10 . λ x11 : (ι → ι) → ι → ι . λ x12 : ι → ι . x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . x14) (λ x13 . x13) (λ x13 : ι → ι → ι . λ x14 x15 . setsum 0 0) (λ x13 : ι → ι . 0) (x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . 0) (λ x13 . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x13 : ι → ι . 0) 0 0)) x4)) = setsum (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0) (λ x9 : ι → ι → ι . λ x10 x11 . 0) (λ x9 : ι → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . 0) (λ x10 . x10)) (setsum 0 (setsum 0 0)) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . x0 (λ x12 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x13 x14 . x13) (λ x12 . 0)) (λ x9 . x3 (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 x15 . 0) (λ x11 . 0) (λ x11 : ι → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0) 0 0) x7 (λ x10 : ι → ι → ι . setsum 0 0) (λ x10 . x2 (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0)))) 0) ⟶ (∀ x4 x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : ι → ι . x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . x0 (λ x14 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 x16 . 0) (λ x14 . 0)) (setsum (setsum (Inj0 (x6 (λ x9 . λ x10 : ι → ι . 0))) (Inj0 0))) (λ x9 : ι → ι → ι . λ x10 x11 . setsum (x3 (λ x12 . setsum 0 0) (x9 0 (setsum 0 0)) (λ x12 : ι → ι → ι . 0) (λ x12 . Inj1 (x9 0 0))) 0) (λ x9 : ι → ι . x6 (λ x10 . λ x11 : ι → ι . x7 (x9 (x3 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . 0) (λ x12 . 0))))) (Inj1 0) (x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . 0) (λ x9 . 0) (λ x9 : ι → ι → ι . λ x10 x11 . Inj1 (x0 (λ x12 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x13 x14 . x14) (λ x12 . x1 (λ x13 : (ι → (ι → ι) → ι) → ι . λ x14 . λ x15 : (ι → ι) → ι . λ x16 x17 . 0) (λ x13 . 0) (λ x13 : ι → ι → ι . λ x14 x15 . 0) (λ x13 : ι → ι . 0) 0 0))) (λ x9 : ι → ι . x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . Inj0 (setsum 0 0)) (Inj1 (setsum 0 0))) 0 0) = x1 (λ x9 : (ι → (ι → ι) → ι) → ι . λ x10 . λ x11 : (ι → ι) → ι . λ x12 x13 . setsum (Inj1 (x2 (λ x14 : ((ι → ι) → ι) → ι → ι → ι . λ x15 . λ x16 : (ι → ι) → ι → ι . λ x17 : ι → ι . λ x18 . x16 (λ x19 . 0) 0) 0)) x12) (λ x9 . Inj0 0) (λ x9 : ι → ι → ι . λ x10 x11 . x10) (λ x9 : ι → ι . x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . 0) (λ x10 . Inj0 (Inj0 (setsum 0 0)))) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . x10) (λ x9 . setsum (x6 (λ x10 . λ x11 : ι → ι . Inj0 0)) (x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . x14) (setsum 0 0)))) (setsum (x3 (λ x9 . Inj0 0) (x3 (λ x9 . 0) (x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . 0) (λ x9 . 0)) (λ x9 : ι → ι → ι . x5 (λ x10 : ι → ι → ι . 0)) (λ x9 . 0)) (λ x9 : ι → ι → ι . 0) (λ x9 . x5 (λ x10 : ι → ι → ι . x3 (λ x11 . 0) 0 (λ x11 : ι → ι → ι . 0) (λ x11 . 0)))) (x6 (λ x9 . λ x10 : ι → ι . x10 x9)))) ⟶ (∀ x4 : ι → (ι → ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι → ι → ι → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . x10) (λ x9 . setsum (setsum (setsum (Inj1 0) 0) (x3 (λ x10 . 0) x7 (λ x10 : ι → ι → ι . setsum 0 0) (λ x10 . Inj0 0))) (x5 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . setsum 0 0) (λ x10 . Inj0 0) (λ x10 : ι → ι → ι . λ x11 x12 . setsum 0 0) (λ x10 : ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x12 x13 . 0) (λ x11 . 0)) 0 0))) = setsum (Inj1 0) 0) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x7 . x0 (λ x9 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x10 x11 . setsum x7 (x2 (λ x12 : ((ι → ι) → ι) → ι → ι → ι . λ x13 . λ x14 : (ι → ι) → ι → ι . λ x15 : ι → ι . λ x16 . x0 (λ x17 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x18 x19 . Inj1 0) (λ x17 . Inj1 0)) (Inj0 (Inj1 0)))) (λ x9 . x3 (λ x10 . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x12 x13 . 0) (setsum (Inj0 0))) (Inj0 (setsum x7 (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x10 . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0) 0 0))) (λ x10 : ι → ι → ι . x0 (λ x11 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x12 x13 . x0 (λ x14 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x15 x16 . x15) (λ x14 . 0)) (λ x11 . x11)) (λ x10 . x9)) = x3 (λ x9 . x6 (λ x10 . λ x11 : ι → ι . x9) x9 (x6 (λ x10 . λ x11 : ι → ι . 0) (x6 (λ x10 . λ x11 : ι → ι . x11 0) (Inj1 0) (setsum 0 0) (x0 (λ x10 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . λ x11 x12 . 0) (λ x10 . 0))) (x3 (λ x10 . 0) x7 (λ x10 : ι → ι → ι . setsum 0 0) (λ x10 . x1 (λ x11 : (ι → (ι → ι) → ι) → ι . λ x12 . λ x13 : (ι → ι) → ι . λ x14 x15 . 0) (λ x11 . 0) (λ x11 : ι → ι → ι . λ x12 x13 . 0) (λ x11 : ι → ι . 0) 0 0)) (x6 (λ x10 . λ x11 : ι → ι . setsum 0 0) 0 (Inj1 0) (x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x10 . 0) (λ x10 : ι → ι → ι . λ x11 x12 . 0) (λ x10 : ι → ι . 0) 0 0))) 0) (x6 (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ((ι → ι) → ι) → ι → ι → ι . λ x12 . λ x13 : (ι → ι) → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 (setsum 0 0)) x9) (x3 (λ x9 . x1 (λ x10 : (ι → (ι → ι) → ι) → ι . λ x11 . λ x12 : (ι → ι) → ι . λ x13 x14 . 0) (λ x10 . x9) (λ x10 : ι → ι → ι . λ x11 x12 . Inj0 0) (λ x10 : ι → ι . x9) (x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0) 0) (x5 (λ x9 x10 x11 . setsum 0 0)) (λ x9 : ι → ι → ι . x9 (Inj0 0) (x6 (λ x10 . λ x11 : ι → ι . 0) 0 0 0)) (λ x9 . x6 (λ x10 . λ x11 : ι → ι . x3 (λ x12 . 0) 0 (λ x12 : ι → ι → ι . 0) (λ x12 . 0)) 0 x7 (Inj1 0))) (x5 (λ x9 x10 x11 . Inj0 0)) x7) (λ x9 : ι → ι → ι . Inj0 (x5 (λ x10 x11 x12 . setsum (Inj1 0) (Inj0 0)))) (λ x9 . x3 (λ x10 . Inj0 x9) (x2 (λ x10 : ((ι → ι) → ι) → ι → ι → ι . λ x11 . λ x12 : (ι → ι) → ι → ι . λ x13 : ι → ι . λ x14 . 0) (x5 (λ x10 x11 x12 . x12))) (λ x10 : ι → ι → ι . Inj1 (x10 0 (Inj1 0))) (λ x10 . 0))) ⟶ False (proof)
Theorem 92643.. : ∀ x0 : (ι → ι → ι) → ι → ι . ∀ x1 : (ι → ι) → ι → ι → (ι → ι) → ι → ι . ∀ x2 : ((ι → (ι → ι → ι) → ι) → ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ((ι → ι) → ι) → ι → ι . x3 (λ x9 . x3 (λ x10 . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 . x0 (λ x13 x14 . x11 0 (λ x15 x16 . 0)) (setsum 0 0)) (x3 (λ x11 . x11) x6)) (x1 (λ x10 . x7 (λ x11 : (ι → ι) → ι . 0) (λ x11 : ι → ι . Inj0 0) (setsum 0 0)) 0 (x0 (λ x10 x11 . x9) x9) (λ x10 . Inj0 0) (Inj0 (setsum 0 0)))) (x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 . setsum (x9 (Inj0 0) (λ x11 x12 . 0)) (setsum (x1 (λ x11 . 0) 0 0 (λ x11 . 0) 0) (setsum 0 0))) x5) = x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 . Inj0 0) (x4 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . setsum (Inj0 0) 0) (x7 (λ x9 : (ι → ι) → ι . 0) (λ x9 : ι → ι . x7 (λ x10 : (ι → ι) → ι . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 . 0) 0) (λ x10 : ι → ι . x1 (λ x11 . 0) 0 0 (λ x11 . 0) 0) 0) (Inj1 x6)) (λ x9 . x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 . setsum (Inj0 0) (x10 0 (λ x12 x13 . 0))) (Inj0 (setsum 0 0))) (setsum x5 (x1 (λ x9 . x3 (λ x10 . 0) 0) (setsum 0 0) (setsum 0 0) (λ x9 . 0) (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 . Inj1 0) (x0 (λ x9 x10 . x3 (λ x11 . setsum 0 (x1 (λ x12 . 0) 0 0 (λ x12 . 0) 0)) (x3 (λ x11 . x0 (λ x12 x13 . 0) 0) 0)) x4) = Inj1 x7) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 . Inj0 (x1 (λ x11 . x9 (x9 0 (λ x12 x13 . 0)) (λ x12 x13 . setsum 0 0)) (Inj1 (setsum 0 0)) (x3 (λ x11 . Inj1 0) (setsum 0 0)) (λ x11 . x11) 0)) 0 = Inj1 (x4 (x3 (λ x9 . 0) (Inj0 (setsum 0 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 : ι → (ι → ι → ι) → ι . λ x10 . setsum (Inj0 (Inj0 (x9 0 (λ x11 x12 . 0)))) (x3 (λ x11 . setsum (Inj0 0) (x3 (λ x12 . 0) 0)) x7)) (x0 (λ x9 x10 . 0) (setsum x4 (Inj1 (x1 (λ x9 . 0) 0 0 (λ x9 . 0) 0)))) = x0 (λ x9 x10 . Inj1 x7) (setsum (setsum (x6 0) (x1 (λ x9 . setsum 0 0) (setsum 0 0) (Inj0 0) (λ x9 . x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 . 0) 0) (setsum 0 0))) x4)) ⟶ (∀ x4 x5 . ∀ x6 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . 0) 0 0 (λ x9 . x6 x5 (λ x10 x11 . 0) (λ x10 . x9)) (x0 (λ x9 x10 . Inj1 (Inj1 (setsum 0 0))) (setsum (Inj1 0) (x1 (λ x9 . x1 (λ x10 . 0) 0 0 (λ x10 . 0) 0) 0 0 (λ x9 . 0) (x0 (λ x9 x10 . 0) 0)))) = x0 (λ x9 x10 . x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 . 0) (setsum x10 (x3 (λ x11 . 0) (x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 . 0) 0)))) (Inj0 (Inj1 x4))) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . Inj1 0) (x3 (λ x9 . x2 (λ x10 : ι → (ι → ι → ι) → ι . λ x11 . x7) 0) 0) 0 (λ x9 . x6) (Inj1 (setsum (Inj1 (setsum 0 0)) 0)) = Inj1 (x3 (λ x9 . 0) (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι → ι → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι) → ι) → ι → ι → ι . ∀ x7 . x0 (λ x9 x10 . x1 (λ x11 . x1 (λ x12 . x11) (x3 (λ x12 . Inj0 0) (x1 (λ x12 . 0) 0 0 (λ x12 . 0) 0)) (x0 (λ x12 x13 . x2 (λ x14 : ι → (ι → ι → ι) → ι . λ x15 . 0) 0) x7) (λ x12 . x3 (λ x13 . x12) (Inj1 0)) x7) (x0 (λ x11 x12 . setsum (x0 (λ x13 x14 . 0) 0) x11) 0) x7 (x2 (λ x11 : ι → (ι → ι → ι) → ι . λ x12 . x1 (λ x13 . x3 (λ x14 . 0) 0) 0 (x11 0 (λ x13 x14 . 0)) (λ x13 . setsum 0 0) 0)) 0) (Inj0 (Inj0 (x3 (λ x9 . 0) (x6 (λ x9 : (ι → ι) → ι . 0) 0 0)))) = Inj0 x7) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 x10 . setsum 0 0) (setsum 0 0) = x7) ⟶ False (proof)
Theorem cbf3a.. : ∀ x0 : (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 → ι) → ι → ι) → (ι → ι) → ι → ι . ∀ x3 : (ι → ι) → ι → ι . (∀ x4 : ι → (ι → ι) → (ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι) → ι) → (ι → ι) → (ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 . 0) (setsum 0 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x3 (λ x16 . 0) 0) 0 (x7 0 (λ x11 x12 . 0)) (λ x11 : ι → ι . λ x12 . x10 0 (λ x13 . 0) 0) (λ x11 . setsum 0 0) 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . setsum (x9 0 (λ x11 . 0) 0) 0))) = x6 (λ x9 : (ι → ι) → ι . x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . 0) (λ x10 . x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . x11) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . x10))) (λ x9 . setsum (x5 (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . x11 0 (λ x12 . 0) 0) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . setsum 0 0)) (λ x10 . x9)) (x6 (λ x10 : (ι → ι) → ι . x9) (λ x10 . x10) (λ x10 . 0) (x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . x3 (λ x15 . 0) 0) (setsum 0 0) (Inj0 0) (λ x10 : ι → ι . λ x11 . 0) (λ x10 . Inj1 0) x9))) Inj1 (Inj1 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . 0)))) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x3 (λ x9 . 0) (x6 (λ x9 . x6 (λ x10 . 0))) = setsum (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . Inj1 (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x1 (λ x16 . λ x17 : ι → ι . λ x18 : ι → ι → ι . λ x19 . 0) (λ x16 . 0)) 0 (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) 0) (λ x11 : ι → ι . λ x12 . x12) (λ x11 . x11) 0)) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . setsum (setsum (setsum 0 0) 0) (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x0 (λ x16 . λ x17 : ι → (ι → ι) → ι → ι . 0) (λ x16 : ι → (ι → ι) → ι → ι . λ x17 : (ι → ι) → ι . 0)) (x10 (λ x11 . 0)) (setsum 0 0) (λ x11 : ι → ι . λ x12 . x12) (λ x11 . Inj0 0) (x6 (λ x11 . 0))))) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . 0) (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . x6 (λ x10 . x6 (λ x11 . 0)))) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . 0) (x5 0 (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . 0)) (x4 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0))) (x3 (λ x9 . 0) 0) (λ x9 : ι → ι . λ x10 . x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . setsum 0 0) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . 0)) (λ x9 . Inj0 0) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . x0 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → (ι → ι) → ι → ι . λ x15 : (ι → ι) → ι . 0)) (x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . 0) 0 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) 0) 0 (λ x9 : ι → ι . λ x10 . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . 0) 0 0 (λ x11 : ι → ι . λ x12 . 0) (λ x11 . 0) 0) (λ x9 . x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . 0) 0 0 (λ x10 : ι → ι . λ x11 . 0) (λ x10 . 0) 0) (x4 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0)))) (λ x9 : ι → ι . x9) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . x12 0 (x11 0)) (λ x10 . x3 (λ x11 . 0) x9)) 0)) ⟶ (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x7 . x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 . 0) (λ x14 . x12 (x12 0))) (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . x3 (λ x15 . Inj1 0) (x13 0 0)) (λ x11 . x7))) 0 (λ x9 : ι → ι . λ x10 . 0) (λ x9 . 0) (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . 0)) = x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 . x18) (λ x15 . 0)) (λ x11 . x11)) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . Inj1 (x9 (Inj0 (x10 (λ x11 . 0))) (λ x11 . setsum 0 0) (setsum (x0 (λ x11 . λ x12 : ι → (ι → ι) → ι → ι . 0) (λ x11 : ι → (ι → ι) → ι → ι . λ x12 : (ι → ι) → ι . 0)) x7)))) ⟶ (∀ x4 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . setsum (x3 (λ x14 . Inj0 x11) 0) (Inj1 (Inj1 x13))) (x4 (λ x9 : (ι → ι) → ι → ι . 0)) (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . x11 0 (x2 (λ x13 x14 x15 . λ x16 : ι → ι . λ x17 . x3 (λ x18 . 0) 0) 0 (x11 0 0) (λ x13 : ι → ι . λ x14 . Inj0 0) (λ x13 . setsum 0 0) 0)) (λ x9 . x6)) (λ x9 : ι → ι . λ x10 . x10) (λ x9 . 0) (Inj1 (Inj0 x7)) = x4 (λ x9 : (ι → ι) → ι → ι . Inj0 (x5 (x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . 0) 0 (setsum 0 0) (λ x10 : ι → ι . λ x11 . x1 (λ x12 . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 . 0) (λ x12 . 0)) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . 0) (λ x11 . 0)) 0)))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . x2 (λ x13 x14 x15 . λ x16 : ι → ι . λ x17 . x1 (λ x18 . λ x19 : ι → ι . λ x20 : ι → ι → ι . λ x21 . x19 0) (λ x18 . 0)) (x10 (x1 (λ x13 . λ x14 : ι → ι . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 . 0))) (Inj0 0) (λ x13 : ι → ι . λ x14 . 0) (λ x13 . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . x12) (λ x14 . Inj1 0) (Inj0 0)) 0) (λ x9 . setsum (x7 (x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . Inj1 0) (x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . 0) (λ x10 . 0)) x9 (λ x10 : ι → ι . λ x11 . setsum 0 0) (λ x10 . Inj0 0) 0)) (x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . setsum (setsum 0 0) 0) (λ x10 . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . x15) 0 (Inj1 0) (λ x11 : ι → ι . λ x12 . x9) (λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . 0)) x9))) = x2 (λ x9 x10 x11 . λ x12 : ι → ι . λ x13 . x1 (λ x14 . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 . 0) (λ x14 . x13)) (Inj0 (setsum 0 (setsum (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . 0)) 0))) (setsum (x5 (Inj1 x4)) (Inj0 (x3 (λ x9 . x7 0) (setsum 0 0)))) (λ x9 : ι → ι . λ x10 . x9 (x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . 0) (λ x11 . x9 (x9 0)))) (λ x9 . Inj0 (x0 (λ x10 . λ x11 : ι → (ι → ι) → ι → ι . x3 (λ x12 . x1 (λ x13 . λ x14 : ι → ι . λ x15 : ι → ι → ι . λ x16 . 0) (λ x13 . 0)) (x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . 0))) (λ x10 : ι → (ι → ι) → ι → ι . λ x11 : (ι → ι) → ι . x2 (λ x12 x13 x14 . λ x15 : ι → ι . λ x16 . 0) (Inj0 0) x9 (λ x12 : ι → ι . λ x13 . x13) (λ x12 . x12) (setsum 0 0)))) (x3 (λ x9 . x7 0) (x7 x4))) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 x6 : ι → ι → (ι → ι) → ι . ∀ x7 : (ι → ι) → ι → ι . x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . setsum (setsum (x2 (λ x10 x11 x12 . λ x13 : ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 . 0) (λ x15 . 0)) (x6 0 0 (λ x10 . 0)) (Inj1 0) (λ x10 : ι → ι . λ x11 . x9) (λ x10 . x1 (λ x11 . λ x12 : ι → ι . λ x13 : ι → ι → ι . λ x14 . 0) (λ x11 . 0)) 0) (setsum (Inj1 0) (x3 (λ x10 . 0) 0))) (x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . x12 (x0 (λ x14 . λ x15 : ι → (ι → ι) → ι → ι . 0) (λ x14 : ι → (ι → ι) → ι → ι . λ x15 : (ι → ι) → ι . 0)) (x1 (λ x14 . λ x15 : ι → ι . λ x16 : ι → ι → ι . λ x17 . 0) (λ x14 . 0))) (λ x10 . 0))) = setsum (setsum 0 (Inj1 (Inj1 (x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . 0))))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . setsum (Inj0 (x10 (setsum 0 0) (λ x11 . x1 (λ x12 . λ x13 : ι → ι . λ x14 : ι → ι → ι . λ x15 . 0) (λ x12 . 0)) 0)) (x3 (λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . 0) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . x2 (λ x14 x15 x16 . λ x17 : ι → ι . λ x18 . 0) 0 0 (λ x14 : ι → ι . λ x15 . 0) (λ x14 . 0) 0)) (x10 (Inj0 0) (λ x11 . 0) (setsum 0 0)))) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . Inj0 (x3 (λ x11 . x7) 0)) = x6 (x1 (λ x9 . λ x10 : ι → ι . λ x11 : ι → ι → ι . λ x12 . 0) (λ x9 . x1 (λ x10 . λ x11 : ι → ι . λ x12 : ι → ι → ι . λ x13 . 0) (λ x10 . Inj0 0)))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι . ∀ x6 : (ι → ι → ι → ι) → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x9 . λ x10 : ι → (ι → ι) → ι → ι . x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . Inj1 (setsum (setsum 0 0) x13)) 0 (setsum 0 (x2 (λ x11 x12 x13 . λ x14 : ι → ι . λ x15 . setsum 0 0) 0 (setsum 0 0) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . x9) (x10 0 (λ x11 . 0) 0))) (λ x11 : ι → ι . λ x12 . 0) (λ x11 . x10 x11 (λ x12 . x2 (λ x13 x14 x15 . λ x16 : ι → ι . λ x17 . x16 0) 0 x12 (λ x13 : ι → ι . λ x14 . x1 (λ x15 . λ x16 : ι → ι . λ x17 : ι → ι → ι . λ x18 . 0) (λ x15 . 0)) (λ x13 . Inj1 0) 0) x11) 0) (λ x9 : ι → (ι → ι) → ι → ι . λ x10 : (ι → ι) → ι . x7) = setsum (setsum 0 x4) (x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 . λ x13 : ι → (ι → ι) → ι → ι . setsum (Inj1 0) (x13 0 (λ x14 . 0) 0)) (λ x12 : ι → (ι → ι) → ι → ι . λ x13 : (ι → ι) → ι . 0)) 0)) ⟶ False (proof)
Theorem 66876.. : ∀ x0 : (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) → ι . ∀ x3 : ((ι → ι) → ι) → ι → ((ι → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι . (∀ x4 . ∀ x5 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . 0) x7 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . x1 (λ x15 . 0) (λ x15 : ι → ι → ι → ι . Inj1 0) x13 (λ x15 . x1 (λ x16 . 0) (λ x16 : ι → ι → ι → ι . 0) 0 (λ x16 . 0))) x11 (λ x14 . x0 (λ x15 . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 x18 x19 . x3 (λ x20 : ι → ι . 0) 0 (λ x20 : ι → ι → ι . λ x21 : ι → ι . λ x22 . 0) 0 0) (λ x15 . x14) (x0 (λ x15 . λ x16 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x17 x18 x19 . 0) (λ x15 . 0) 0 0 (λ x15 . 0)) (setsum 0 0) (λ x15 . setsum 0 0))) (λ x9 . x3 (λ x10 : ι → ι . x3 (λ x11 : ι → ι . x2 (λ x12 : ι → ι . 0) (λ x12 x13 : (ι → ι) → ι . 0)) (x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 (λ x11 . 0)) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) (Inj1 0) (x6 0)) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x3 (λ x13 : ι → ι . 0) (Inj0 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . setsum 0 0) (x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 (λ x13 . 0)) (Inj1 0)) 0 x7) (x5 (λ x9 x10 : ι → ι . λ x11 . x10 (x10 0))) x4 (λ x9 . x7)) (x6 0) = x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 . setsum 0) (λ x9 . x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . x1 (λ x11 . x10 0 0 0) (λ x11 : ι → ι → ι → ι . 0) (x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0)) (λ x11 . x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0) 0 (λ x12 . 0))) (x1 (λ x10 . setsum 0 0) (λ x10 : ι → ι → ι → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0) 0 0 (λ x11 . 0)) 0 (λ x10 . 0)) (λ x10 . x9)) (λ x10 . x7)) (Inj0 (x2 (λ x9 : ι → ι . x6 (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0) 0 0 (λ x10 . 0))) (λ x9 x10 : (ι → ι) → ι . setsum x7 0))) (setsum (setsum 0 0) x7) (λ x9 . setsum 0 (setsum 0 (setsum (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . 0)) x7)))) ⟶ (∀ x4 : (ι → ι → ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → (ι → ι) → ι → ι . ∀ x7 . x3 (λ x9 : ι → ι . x9 (setsum x5 0)) (x4 (λ x9 x10 x11 . 0) (λ x9 . setsum x7 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . setsum 0 (setsum (setsum 0 0) 0)) (λ x12 . Inj0 (setsum 0 (setsum 0 0))) (x0 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . x13 (λ x17 : ι → ι . setsum 0 0) (λ x17 . x14) 0) (λ x12 . x11) (setsum x11 (x9 0 0)) (setsum x7 0) (λ x12 . 0)) (x2 (λ x12 : ι → ι . x11) (λ x12 x13 : (ι → ι) → ι . 0)) (λ x12 . x10 0)) (x6 0 (λ x9 x10 . x7) (λ x9 . 0) (x4 (λ x9 x10 x11 . x10) (λ x9 . x7))) (x3 (λ x9 : ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . x7) (x6 0 (λ x10 x11 . Inj1 0) (λ x10 . x6 0 (λ x11 x12 . 0) (λ x11 . 0) 0) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0) 0 0 (λ x10 . 0))) (x2 (λ x10 : ι → ι . Inj1 0) (λ x10 x11 : (ι → ι) → ι . 0)) (λ x10 . x3 (λ x11 : ι → ι . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . 0) (λ x12 . 0) 0 0 (λ x12 . 0)) (setsum 0 0) (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj1 0) (x6 0 (λ x11 x12 . 0) (λ x11 . 0) 0) (Inj0 0))) (setsum (x1 (λ x9 . setsum 0 0) (λ x9 : ι → ι → ι → ι . x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0) (x2 (λ x9 : ι → ι . 0) (λ x9 x10 : (ι → ι) → ι . 0)) (λ x9 . setsum 0 0)) x5) (λ x9 : ι → ι → ι . λ x10 : ι → ι . Inj0) 0 0) = setsum (x3 (λ x9 : ι → ι . Inj0 (x3 (λ x10 : ι → ι . x9 0) x5 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) (x6 0 (λ x10 x11 . 0) (λ x10 . 0) 0) (Inj0 0))) x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj1 0) (x3 (λ x9 : ι → ι . setsum 0 (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0)) (x1 (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)) (λ x9 : ι → ι → ι → ι . 0) x5 (λ x9 . 0)) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . Inj1 0) 0 (Inj1 (x2 (λ x9 : ι → ι . 0) (λ x9 x10 : (ι → ι) → ι . 0)))) (x4 (λ x9 x10 x11 . Inj0 0) (λ x9 . x6 (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0) (λ x10 x11 . Inj1 0) (λ x10 . 0) (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0)))) x7) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 . ∀ x7 : ((ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . x2 (λ x9 : ι → ι . x9 (setsum 0 0)) (λ x9 x10 : (ι → ι) → ι . x2 (λ x11 : ι → ι . setsum 0 (setsum (x11 0) (Inj0 0))) (λ x11 x12 : (ι → ι) → ι . x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . x13 (x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . 0) 0 (λ x14 . 0)) (x3 (λ x14 : ι → ι . 0) 0 (λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . 0) 0 0)) (x0 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . Inj1 0) (λ x13 . x13) (setsum 0 0) (x0 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . 0) (λ x13 . 0) 0 0 (λ x13 . 0)) (λ x13 . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . 0) 0 (λ x14 . 0))) (λ x13 . 0))) = Inj0 (x4 (λ x9 . 0))) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι → ι) → ι . x2 (λ x9 : ι → ι . x9 0) (λ x9 x10 : (ι → ι) → ι . x9 (λ x11 . 0)) = x5) ⟶ (∀ x4 x5 : ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . setsum 0 x13) (λ x10 . Inj0 (x3 (λ x11 : ι → ι . Inj0 0) x9 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 x9)) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . setsum x9 (x2 (λ x12 : ι → ι . 0) (λ x12 x13 : (ι → ι) → ι . 0)))) (x1 (λ x10 . x3 (λ x11 : ι → ι . x9) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj1 0) (x3 (λ x11 : ι → ι . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0) (x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 (λ x11 . 0))) (λ x10 : ι → ι → ι → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . x14) (λ x11 . x10 0 0 0) (x6 (λ x11 : (ι → ι) → ι → ι . 0) (λ x11 . 0)) (setsum 0 0) (λ x11 . setsum 0 0)) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . x13) (λ x10 . x1 (λ x11 . 0) (λ x11 : ι → ι → ι → ι . 0) 0 (λ x11 . 0)) (x6 (λ x10 : (ι → ι) → ι → ι . 0) (λ x10 . 0)) (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0) (λ x10 . 0)) (λ x10 . 0)) (λ x10 . x7)) (λ x9 : ι → ι → ι → ι . x6 (λ x10 : (ι → ι) → ι → ι . x2 (λ x11 : ι → ι . x7) (λ x11 x12 : (ι → ι) → ι . 0)) (λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 x16 . setsum 0 0) (λ x12 . 0) (x9 0 0 0) 0 (λ x12 . 0)) (λ x11 . 0))) 0 (λ x9 . x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . x3 (λ x12 : ι → ι . x3 (λ x13 : ι → ι . x1 (λ x14 . 0) (λ x14 : ι → ι → ι → ι . 0) 0 (λ x14 . 0)) x9 (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . x1 (λ x16 . 0) (λ x16 : ι → ι → ι → ι . 0) 0 (λ x16 . 0)) 0 (setsum 0 0)) 0 (λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x14) 0 0)) = x2 (λ x9 : ι → ι . setsum (x3 (λ x10 : ι → ι . x9 (x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0))) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . x10 (λ x12 . 0))) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 0) (x3 (λ x10 : ι → ι . x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0)) (setsum 0 0) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . 0) (λ x13 . 0) 0 0 (λ x13 . 0)) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . 0)) 0) 0) 0) (λ x9 x10 : (ι → ι) → ι . x9 (λ x11 . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι → ι . ∀ x7 . x1 (λ x9 . setsum (Inj1 x7) (setsum (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . x12) (λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . 0) 0) (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . 0)) 0 (λ x10 . x6 (λ x11 : (ι → ι) → ι → ι . 0) 0)) (setsum 0 (x5 0 0 (λ x10 . 0))))) (λ x9 : ι → ι → ι → ι . 0) (setsum 0 0) (λ x9 . x7) = setsum (Inj0 (x5 (x5 0 (x3 (λ x9 : ι → ι . 0) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . 0) 0 0) (λ x9 . setsum 0 0)) (x1 (λ x9 . Inj1 0) (λ x9 : ι → ι → ι → ι . x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . 0) (λ x10 . 0) 0 0 (λ x10 . 0)) (setsum 0 0) (λ x9 . x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0)) (λ x9 . x9))) 0) ⟶ (∀ x4 : ((ι → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → ι → ι . ∀ x6 . ∀ x7 : (((ι → ι) → ι) → (ι → ι) → ι) → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x13) (λ x9 . setsum (x7 (λ x10 : (ι → ι) → ι . λ x11 : ι → ι . x11 (x1 (λ x12 . 0) (λ x12 : ι → ι → ι → ι . 0) 0 (λ x12 . 0)))) (x1 (λ x10 . x6) (λ x10 : ι → ι → ι → ι . x3 (λ x11 : ι → ι . x9) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . Inj0 0) (x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0)) (x0 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . 0) (λ x11 . 0) 0 0 (λ x11 . 0))) (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . x9)) (λ x10 . setsum x9 (x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0))))) (setsum (Inj0 (setsum (setsum 0 0) (x1 (λ x9 . 0) (λ x9 : ι → ι → ι → ι . 0) 0 (λ x9 . 0)))) (x7 (λ x9 : (ι → ι) → ι . λ x10 : ι → ι . 0))) (x3 (λ x9 : ι → ι . Inj1 0) 0 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 . λ x13 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x14 x15 . Inj1) (λ x12 . x3 (λ x13 : ι → ι . setsum 0 0) (setsum 0 0) (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) (Inj0 0) (setsum 0 0)) 0 (setsum (x2 (λ x12 : ι → ι . 0) (λ x12 x13 : (ι → ι) → ι . 0)) x11) (λ x12 . 0)) x6 (x4 (λ x9 x10 : ι → ι . λ x11 . x1 (λ x12 . x2 (λ x13 : ι → ι . 0) (λ x13 x14 : (ι → ι) → ι . 0)) (λ x12 : ι → ι → ι → ι . setsum 0 0) (Inj1 0) (λ x12 . 0)))) (λ x9 . 0) = Inj0 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . Inj0 (Inj0 (x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . x3 (λ x19 : ι → ι . 0) 0 (λ x19 : ι → ι → ι . λ x20 : ι → ι . λ x21 . 0) 0 0) (λ x14 . 0) 0 (x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (λ x14 . x2 (λ x15 : ι → ι . 0) (λ x15 x16 : (ι → ι) → ι . 0))))) (λ x9 . x5) (Inj0 x5) (Inj0 x6) (λ x9 . x3 (λ x10 : ι → ι . setsum (x7 x9 (λ x11 : ι → ι . λ x12 . x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 (λ x13 . 0)) 0 (x2 (λ x11 : ι → ι . 0) (λ x11 x12 : (ι → ι) → ι . 0))) (setsum x6 (Inj1 0))) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . x3 (λ x15 : ι → ι . x14) x12 (λ x15 : ι → ι → ι . λ x16 : ι → ι . λ x17 . Inj1 0) 0 x13) (λ x10 . x9) 0 (setsum (setsum 0 0) 0) (λ x10 . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . x1 (λ x16 . 0) (λ x16 : ι → ι → ι → ι . 0) 0 (λ x16 . 0)) (λ x11 . x11) 0 x10 (λ x11 . x9))) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . Inj0 x9) (x3 (λ x10 : ι → ι . x0 (λ x11 . λ x12 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x13 x14 x15 . x12 (λ x16 : ι → ι . 0) (λ x16 . 0) 0) (λ x11 . 0) (x7 0 (λ x11 : ι → ι . λ x12 . 0) 0 0) 0 (λ x11 . Inj1 0)) (x7 (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . 0)) (λ x10 : ι → ι . λ x11 . x9) 0 (setsum 0 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x12) (x2 (λ x10 : ι → ι . Inj1 0) (λ x10 x11 : (ι → ι) → ι . 0)) (x2 (λ x10 : ι → ι . 0) (λ x10 x11 : (ι → ι) → ι . x11 (λ x12 . 0)))) (x3 (λ x10 : ι → ι . setsum (setsum 0 0) x9) x9 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 (x7 (setsum 0 0) (λ x10 : ι → ι . λ x11 . x7 0 (λ x12 : ι → ι . λ x13 . 0) 0 0) x5 (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . 0))))) = setsum (x1 (λ x9 . x3 (λ x10 : ι → ι . x7 x6 (λ x11 : ι → ι . λ x12 . x9) (x10 0) (setsum 0 0)) (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . x11 (λ x15 : ι → ι . 0) (λ x15 . 0) 0) (λ x10 . setsum 0 0) x5 (setsum 0 0) (λ x10 . setsum 0 0)) (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . x11 (x10 0 0)) x9 x9) (λ x9 : ι → ι → ι → ι . x7 (Inj0 (setsum 0 0)) (λ x10 : ι → ι . λ x11 . Inj1 0) 0 (x0 (λ x10 . λ x11 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x12 x13 x14 . Inj0 0) (λ x10 . setsum 0 0) 0 (setsum 0 0) (λ x10 . Inj0 0))) x5 (λ x9 . 0)) (x3 (λ x9 : ι → ι . 0) (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . Inj0 0) (λ x9 . setsum x6 (setsum 0 0)) 0 (x2 (λ x9 : ι → ι . x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0) (λ x9 x10 : (ι → ι) → ι . x3 (λ x11 : ι → ι . 0) 0 (λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0)) (λ x9 . setsum (x1 (λ x10 . 0) (λ x10 : ι → ι → ι → ι . 0) 0 (λ x10 . 0)) (x3 (λ x10 : ι → ι . 0) 0 (λ x10 : ι → ι → ι . λ x11 : ι → ι . λ x12 . 0) 0 0))) (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x1 (λ x12 . x9 (x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) 0 0) (Inj0 0)) (λ x12 : ι → ι → ι → ι . x3 (λ x13 : ι → ι . 0) 0 (λ x13 : ι → ι → ι . λ x14 : ι → ι . λ x15 . 0) (x1 (λ x13 . 0) (λ x13 : ι → ι → ι → ι . 0) 0 (λ x13 . 0)) (setsum 0 0)) (x9 0 x11) (λ x12 . x0 (λ x13 . λ x14 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x15 x16 x17 . x1 (λ x18 . 0) (λ x18 : ι → ι → ι → ι . 0) 0 (λ x18 . 0)) (λ x13 . 0) (Inj1 0) 0 (λ x13 . 0))) x6 (x0 (λ x9 . λ x10 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x11 x12 x13 . x3 (λ x14 : ι → ι . setsum 0 0) (x0 (λ x14 . λ x15 : ((ι → ι) → ι) → (ι → ι) → ι → ι . λ x16 x17 x18 . 0) (λ x14 . 0) 0 0 (λ x14 . 0)) (λ x14 : ι → ι → ι . λ x15 : ι → ι . λ x16 . x14 0 0) (Inj1 0) (Inj1 0)) (λ x9 . 0) (Inj0 0) (Inj1 0) (λ x9 . Inj0 (setsum 0 0))))) ⟶ False (proof)
Theorem ccabb.. : ∀ x0 : ((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 → ι . ∀ x3 : ((ι → ι) → ι) → (ι → (ι → ι) → ι) → ι . (∀ x4 x5 . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 : ((ι → ι) → ι) → ι . x3 (λ x9 : ι → ι . 0) (λ x9 . λ x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 : (ι → ι → ι) → ι . x3 (λ x13 : ι → ι . x13 (x12 (λ x14 x15 . 0))) (λ x13 . λ x14 : ι → ι . x12 (λ x15 x16 . x1 (λ x17 . λ x18 : ι → ι . 0) (λ x17 x18 x19 x20 . 0) (λ x17 : ι → ι . 0) 0))) x9 0) = x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . setsum 0 0) (Inj0 (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . Inj1 (x7 (λ x11 : ι → ι . 0))) 0 0)) (setsum (x3 (λ x9 : ι → ι . x9 (x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . 0) 0)) (λ x9 . λ x10 : ι → ι . 0)) 0)) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x3 (λ x9 : ι → ι . Inj1 (setsum x6 (setsum 0 0))) (λ x9 . λ x10 : ι → ι . 0) = x5 (λ x9 : (ι → ι) → ι → ι . x6)) ⟶ (∀ x4 : (ι → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x5 x6 : ι → ι . ∀ x7 : ι → ι → ι . x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (x6 (x1 (λ x9 . λ x10 : ι → ι . x3 (λ x11 : ι → ι . setsum 0 0) (λ x11 . λ x12 : ι → ι . x12 0)) (λ x9 x10 x11 x12 . x12) (λ x9 : ι → ι . 0) (setsum (setsum 0 0) (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . 0) 0 0)))) = setsum (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . x9) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . Inj0 0) (x9 0) 0) (Inj0 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) (x4 (λ x9 x10 x11 . 0) 0 (λ x9 . 0))))) 0) ⟶ (∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 . x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum (x9 x11 (λ x13 : ι → ι . x11)) (x0 (λ x13 : ι → ι . λ x14 : (ι → ι → ι) → ι . x0 (λ x15 : ι → ι . λ x16 : (ι → ι → ι) → ι . x13 0) 0 (x2 (λ x15 : ι → ((ι → ι) → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0)) 0 (x2 (λ x13 : ι → ((ι → ι) → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . setsum 0 0) (x3 (λ x13 : ι → ι . 0) (λ x13 . λ x14 : ι → ι . 0))))) x7 = x7) ⟶ (∀ x4 x5 x6 x7 . x1 (λ x9 . λ x10 : ι → ι . setsum (x10 x9) (x10 (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . Inj1 0) (setsum 0 0)))) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . 0) (Inj1 (Inj1 0)) = Inj1 (Inj0 (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . Inj0 0) (x1 (λ x9 . λ x10 : ι → ι . 0) (λ x9 x10 x11 x12 . x11) (λ x9 : ι → ι . x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . 0) (λ x10 : ι → ι . 0) 0) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) 0)) (x3 (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . 0) 0 0) (λ x9 . λ x10 : ι → ι . Inj1 0))))) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → (ι → ι) → ι . ∀ x6 x7 . x1 (λ x9 . λ x10 : ι → ι . setsum (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0) (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) 0)) (λ x9 x10 x11 x12 . x1 (λ x13 . λ x14 : ι → ι . x2 (λ x15 : ι → ((ι → ι) → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . x3 (λ x19 : ι → ι . x1 (λ x20 . λ x21 : ι → ι . 0) (λ x20 x21 x22 x23 . 0) (λ x20 : ι → ι . 0) 0) (λ x19 . λ x20 : ι → ι . x1 (λ x21 . λ x22 : ι → ι . 0) (λ x21 x22 x23 x24 . 0) (λ x21 : ι → ι . 0) 0)) (Inj1 (Inj0 0))) (λ x13 x14 x15 x16 . x16) (λ x13 : ι → ι . x10) (x2 (λ x13 : ι → ((ι → ι) → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) x12)) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . x0 (λ x12 : ι → ι . λ x13 : (ι → ι → ι) → ι . x2 (λ x14 : ι → ((ι → ι) → ι) → ι . λ x15 : ι → (ι → ι) → ι . λ x16 . λ x17 : ι → ι . 0) (x0 (λ x14 : ι → ι . λ x15 : (ι → ι → ι) → ι . 0) 0 0)) 0 (Inj1 0)) (x9 (Inj1 (x5 0 0 (λ x10 . 0)))) (x1 (λ x10 . λ x11 : ι → ι . 0) (λ x10 x11 x12 x13 . x3 (λ x14 : ι → ι . x3 (λ x15 : ι → ι . 0) (λ x15 . λ x16 : ι → ι . 0)) (λ x14 . λ x15 : ι → ι . x14)) (λ x10 : ι → ι . x9 0) (setsum (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . 0) 0) (Inj0 0)))) (x3 (λ x9 : ι → ι . x9 (x2 (λ x10 : ι → ((ι → ι) → ι) → ι . λ x11 : ι → (ι → ι) → ι . λ x12 . λ x13 : ι → ι . x11 0 (λ x14 . 0)) x7)) (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . x1 (λ x13 . λ x14 : ι → ι . x1 (λ x15 . λ x16 : ι → ι . 0) (λ x15 x16 x17 x18 . 0) (λ x15 : ι → ι . 0) 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι . Inj1 0) x9) (λ x11 x12 x13 x14 . setsum (setsum 0 0) x11) (λ x11 : ι → ι . x7) x9)) = setsum (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . setsum (x10 (λ x11 x12 . x9 0)) (x9 (x0 (λ x11 : ι → ι . λ x12 : (ι → ι → ι) → ι . 0) 0 0))) (setsum (Inj1 (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . 0) 0)) (x3 (λ x9 : ι → ι . Inj0 0) (λ x9 . λ x10 : ι → ι . 0))) (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . x1 (λ x11 . λ x12 : ι → ι . setsum 0 0) (λ x11 x12 x13 x14 . x0 (λ x15 : ι → ι . λ x16 : (ι → ι → ι) → ι . 0) 0 0) (λ x11 : ι → ι . x11 0) (x1 (λ x11 . λ x12 : ι → ι . 0) (λ x11 x12 x13 x14 . 0) (λ x11 : ι → ι . 0) 0)) x7 (x5 (Inj1 0) 0 (λ x9 . Inj0 0)))) 0) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι) → ι . x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . x3 (λ x11 : ι → ι . setsum (setsum (x2 (λ x12 : ι → ((ι → ι) → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) 0) 0) (setsum (x1 (λ x12 . λ x13 : ι → ι . 0) (λ x12 x13 x14 x15 . 0) (λ x12 : ι → ι . 0) 0) (Inj0 0))) (λ x11 . λ x12 : ι → ι . x11)) (x1 (λ x9 . λ x10 : ι → ι . x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . x1 (λ x15 . λ x16 : ι → ι . 0) (λ x15 x16 x17 x18 . 0) (λ x15 : ι → ι . 0) 0) x6)) (λ x9 x10 x11 x12 . setsum (x3 (λ x13 : ι → ι . Inj1 0) (λ x13 . λ x14 : ι → ι . setsum 0 0)) (setsum (setsum 0 0) (x0 (λ x13 : ι → ι . λ x14 : (ι → ι → ι) → ι . 0) 0 0))) (λ x9 : ι → ι . x0 (λ x10 : ι → ι . λ x11 : (ι → ι → ι) → ι . x11 (λ x12 x13 . 0)) (x3 (λ x10 : ι → ι . setsum 0 0) (λ x10 . λ x11 : ι → ι . x2 (λ x12 : ι → ((ι → ι) → ι) → ι . λ x13 : ι → (ι → ι) → ι . λ x14 . λ x15 : ι → ι . 0) 0)) (x7 (λ x10 : ι → ι → ι . setsum 0 0))) (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . setsum (x2 (λ x13 : ι → ((ι → ι) → ι) → ι . λ x14 : ι → (ι → ι) → ι . λ x15 . λ x16 : ι → ι . 0) 0) 0) (setsum 0 0))) (x3 (λ x9 : ι → ι . x9 0) (λ x9 . λ x10 : ι → ι . x1 (λ x11 . λ x12 : ι → ι . setsum (Inj1 0) (x12 0)) (λ x11 x12 x13 x14 . 0) (λ x11 : ι → ι . x7 (λ x12 : ι → ι → ι . setsum 0 0)) (x3 (λ x11 : ι → ι . x10 0) (λ x11 . λ x12 : ι → ι . x1 (λ x13 . λ x14 : ι → ι . 0) (λ x13 x14 x15 x16 . 0) (λ x13 : ι → ι . 0) 0)))) = x1 (λ x9 . λ x10 : ι → ι . x7 (λ x11 : ι → ι → ι . 0)) (λ x9 x10 x11 x12 . setsum (x3 (λ x13 : ι → ι . 0) (λ x13 . λ x14 : ι → ι . setsum (x2 (λ x15 : ι → ((ι → ι) → ι) → ι . λ x16 : ι → (ι → ι) → ι . λ x17 . λ x18 : ι → ι . 0) 0) 0)) x11) (λ x9 : ι → ι . setsum (x5 (λ x10 : (ι → ι) → ι . x10 (λ x11 . setsum 0 0))) x6) (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . x3 (λ x11 : ι → ι . 0) (λ x11 . λ x12 : ι → ι . Inj0 (x3 (λ x13 : ι → ι . 0) (λ x13 . λ x14 : ι → ι . 0)))) (Inj1 0) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι → (ι → ι) → ι . ∀ x5 . ∀ x6 : ((ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 . x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (x1 (λ x9 . λ x10 : ι → ι . x0 (λ x11 : ι → ι . λ x12 : (ι → ι → ι) → ι . 0) 0 (x2 (λ x11 : ι → ((ι → ι) → ι) → ι . λ x12 : ι → (ι → ι) → ι . λ x13 . λ x14 : ι → ι . 0) (Inj0 0))) (λ x9 x10 x11 x12 . 0) (λ x9 : ι → ι . Inj0 (Inj0 0)) (x0 (λ x9 : ι → ι . λ x10 : (ι → ι → ι) → ι . 0) (Inj1 0) x5)) x7 = setsum (x2 (λ x9 : ι → ((ι → ι) → ι) → ι . λ x10 : ι → (ι → ι) → ι . λ x11 . λ x12 : ι → ι . x9 (x0 (λ x13 : ι → ι . λ x14 : (ι → ι → ι) → ι . 0) (x12 0) 0) (λ x13 : ι → ι . x11)) 0) 0) ⟶ False (proof)
Theorem 3f9dd.. : ∀ x0 : (ι → ι) → ι → ι . ∀ x1 : (ι → ι) → (ι → (ι → ι → ι) → ι) → ι . ∀ x2 : ((ι → ι → ι → ι → ι) → ι) → ((((ι → ι) → ι) → ι) → ι → (ι → ι) → ι → ι) → ι → ι . ∀ x3 : (((ι → ι) → ι) → ι) → (ι → ι) → (ι → ι) → ι . (∀ x4 . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (ι → ι) → ι . 0) (λ x9 . x0 (λ x10 . 0) x7) (λ x9 . 0) = setsum 0 x4) ⟶ (∀ x4 . ∀ x5 : ι → (ι → ι) → ι . ∀ x6 x7 . x3 (λ x9 : (ι → ι) → ι . x0 (setsum 0) (setsum x7 (x2 (λ x10 : ι → ι → ι → ι → ι . 0) (λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) 0))) (λ x9 . Inj1 x7) (λ x9 . 0) = setsum (x2 (λ x9 : ι → ι → ι → ι → ι . setsum (x5 (x3 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) (λ x10 . 0)) (λ x10 . x6)) (Inj1 (Inj0 0))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . 0) (Inj1 (x1 (λ x9 . x7) (λ x9 . λ x10 : ι → ι → ι . setsum 0 0)))) (Inj1 0)) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ι → (ι → ι) → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι) → ι → ι → ι) → (ι → ι) → (ι → ι) → ι . x2 (λ x9 : ι → ι → ι → ι → ι . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι . x0 (λ x12 . 0)) 0 = setsum (x0 (λ x9 . setsum x9 (x2 (λ x10 : ι → ι → ι → ι → ι . setsum 0 0) (λ x10 : ((ι → ι) → ι) → ι . λ x11 . λ x12 : ι → ι . λ x13 . 0) (Inj0 0))) (x3 (λ x9 : (ι → ι) → ι . 0) (λ x9 . 0) (λ x9 . x9))) 0) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x2 (λ x9 : ι → ι → ι → ι → ι . Inj1 (x9 0 x7 x7 x7)) (λ x9 : ((ι → ι) → ι) → ι . λ x10 . λ x11 : ι → ι . λ x12 . setsum 0 (x11 (x2 (λ x13 : ι → ι → ι → ι → ι . x2 (λ x14 : ι → ι → ι → ι → ι . 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 . λ x16 : ι → ι . λ x17 . 0) 0) (λ x13 : ((ι → ι) → ι) → ι . λ x14 . λ x15 : ι → ι . λ x16 . x15 0) (x11 0)))) 0 = x6) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x1 (λ x9 . x9) (λ x9 . λ x10 : ι → ι → ι . x9) = setsum (x1 (λ x9 . x5 (λ x10 : ι → ι → ι . Inj0 x7)) (λ x9 . λ x10 : ι → ι → ι . setsum (x1 (λ x11 . setsum 0 0) (λ x11 . λ x12 : ι → ι → ι . x3 (λ x13 : (ι → ι) → ι . 0) (λ x13 . 0) (λ x13 . 0))) (Inj1 (x1 (λ x11 . 0) (λ x11 . λ x12 : ι → ι → ι . 0))))) 0) ⟶ (∀ x4 x5 x6 : ι → ι . ∀ x7 . x1 (λ x9 . x3 (λ x10 : (ι → ι) → ι . x7) (λ x10 . Inj1 (x6 0)) (λ x10 . setsum 0 (x1 (λ x11 . x7) (λ x11 . λ x12 : ι → ι → ι . x11)))) (λ x9 . λ x10 : ι → ι → ι . x9) = x3 (λ x9 : (ι → ι) → ι . setsum (x6 0) (x6 0)) (λ x9 . x6 0) (λ x9 . setsum x9 0)) ⟶ (∀ x4 : ((ι → ι) → ι) → ι . ∀ x5 : (ι → (ι → ι) → ι) → ι . ∀ x6 : ι → ι → ι . ∀ x7 . x0 (λ x9 . Inj0 0) 0 = Inj1 (Inj1 0)) ⟶ (∀ x4 x5 x6 . ∀ x7 : (((ι → ι) → ι) → ι) → ι . x0 (λ x9 . setsum (Inj0 x9) (x3 (λ x10 : (ι → ι) → ι . 0) (λ x10 . 0) (λ x10 . setsum 0 x6))) x4 = x4) ⟶ False (proof)
Theorem 203b5.. : ∀ 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) → ι → ((ι → ι) → ι → ι) → ι . ∀ x2 : (((ι → ι) → (ι → ι → ι) → ι) → ι) → ι → ι . ∀ x3 : (ι → ι) → ((((ι → ι) → ι → ι) → ι) → ι) → (ι → ι) → ι . (∀ x4 : (((ι → ι) → ι → ι) → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x3 (λ x9 . x9) (λ x9 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0) = x5) ⟶ (∀ x4 : ι → ((ι → ι) → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι . ∀ x6 : (ι → (ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ι → ι . x3 (λ x9 . x7 (λ x10 . x10) (Inj1 (Inj0 (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 . 0))))) (λ x9 : ((ι → ι) → ι → ι) → ι . Inj1 (x5 0)) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . Inj0 0)) = x7 (λ x9 . Inj1 (Inj1 0)) (Inj0 0)) ⟶ (∀ x4 . ∀ x5 : (ι → (ι → ι) → ι → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 x7 . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . Inj0 (Inj1 (x5 (λ x10 . λ x11 : ι → ι . λ x12 . x10) (λ x10 x11 . Inj1 0) x6 0))) 0 = Inj1 (Inj0 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι → ι) → ι → (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . x3 (λ x10 . x6 (setsum (x3 (λ x11 . 0) (λ x11 : ((ι → ι) → ι → ι) → ι . 0) (λ x11 . 0)) 0)) (λ x10 : ((ι → ι) → ι → ι) → ι . 0) (λ x10 . setsum 0 0)) (Inj0 0) = setsum (x4 (λ x9 . λ x10 : ι → ι . λ x11 . 0) 0 (λ x9 . setsum (x0 (λ x10 : ι → ι . Inj1 0) (λ x10 : ((ι → ι) → ι → ι) → ι . λ x11 x12 : ι → ι . λ x13 . setsum 0 0)) (x1 (λ x10 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x10 x11 . λ x12 : ι → ι . 0) 0 (λ x10 : ι → ι . λ x11 . x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) 0))) (setsum (x0 (λ x9 : ι → ι . Inj0 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 x11 : ι → ι . λ x12 . 0)) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι . x9 (λ x10 . 0) (λ x10 x11 . 0)) 0))) (x0 (λ x9 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 x11 : ι → ι . λ x12 . x3 (λ x13 . Inj0 0) (λ x13 : ((ι → ι) → ι → ι) → ι . x10 0) (λ x13 . x12)))) ⟶ (∀ x4 : (ι → ι) → ι → ι . ∀ x5 . ∀ x6 : ι → ((ι → ι) → ι) → ι . ∀ x7 : (((ι → ι) → ι) → ι) → ι → ι → ι → ι . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . setsum (x6 (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . x1 (λ x11 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x11 x12 . λ x13 : ι → ι . 0) 0 (λ x11 : ι → ι . λ x12 . 0)) 0) (λ x10 : ι → ι . x3 (λ x11 . setsum 0 0) (λ x11 : ((ι → ι) → ι → ι) → ι . Inj0 0) (λ x11 . 0))) 0) (λ x9 x10 . λ x11 : ι → ι . Inj1 x10) (x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . Inj0 x5) (λ x9 x10 . λ x11 : ι → ι . x7 (λ x12 : (ι → ι) → ι . 0) 0 (setsum (x2 (λ x12 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) x10) (x11 (Inj1 0))) 0 (λ x9 : ι → ι . λ x10 . Inj1 0)) (λ x9 : ι → ι . λ x10 . x0 (λ x11 : ι → ι . x9 0) (λ x11 : ((ι → ι) → ι → ι) → ι . λ x12 x13 : ι → ι . λ x14 . x14)) = Inj1 0) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι → ι) → ι → ι . ∀ x7 . x1 (λ x9 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x9 x10 . λ x11 : ι → ι . x0 (λ x12 : ι → ι . x12 0) (λ x12 : ((ι → ι) → ι → ι) → ι . λ x13 x14 : ι → ι . λ x15 . x14 (Inj0 (x1 (λ x16 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . 0) (λ x16 x17 . λ x18 : ι → ι . 0) 0 (λ x16 : ι → ι . λ x17 . 0))))) (Inj1 0) (λ x9 : ι → ι . λ x10 . 0) = x0 (λ x9 : ι → ι . setsum (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι . Inj0 0) (x6 (λ x10 x11 . x3 (λ x12 . 0) (λ x12 : ((ι → ι) → ι → ι) → ι . 0) (λ x12 . 0)) (setsum 0 0))) (x9 (setsum (setsum 0 0) 0))) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 x11 : ι → ι . λ x12 . setsum (x3 (λ x13 . Inj0 x12) (λ x13 : ((ι → ι) → ι → ι) → ι . x11 x12) (λ x13 . Inj1 x12)) 0)) ⟶ (∀ x4 x5 x6 x7 . x0 (λ x9 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 x11 : ι → ι . λ x12 . setsum (setsum x12 (x1 (λ x13 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι . x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) (λ x13 x14 . λ x15 : ι → ι . x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι . 0) 0) 0 (λ x13 : ι → ι . λ x14 . x11 0))) 0) = Inj0 x5) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι → ι → ι → ι . ∀ x5 x6 x7 . x0 (λ x9 : ι → ι . 0) (λ x9 : ((ι → ι) → ι → ι) → ι . λ x10 x11 : ι → ι . λ x12 . x3 (λ x13 . x13) (λ x13 : ((ι → ι) → ι → ι) → ι . 0) (λ x13 . x0 (λ x14 : ι → ι . Inj0 x13) (λ x14 : ((ι → ι) → ι → ι) → ι . λ x15 x16 : ι → ι . λ x17 . x3 (λ x18 . x3 (λ x19 . 0) (λ x19 : ((ι → ι) → ι → ι) → ι . 0) (λ x19 . 0)) (λ x18 : ((ι → ι) → ι → ι) → ι . x17) (λ x18 . x15 0)))) = setsum (x3 (λ x9 . 0) (λ x9 : ((ι → ι) → ι → ι) → ι . x9 (λ x10 : ι → ι . λ x11 . Inj0 x7)) (λ x9 . x6)) (x3 (λ x9 . x9) (λ x9 : ((ι → ι) → ι → ι) → ι . 0) (λ x9 . 0))) ⟶ False (proof)
Theorem 4d085.. : ∀ x0 : (ι → ι) → (((ι → ι) → ι) → ι) → ι . ∀ x1 : (ι → ι) → ((((ι → ι) → ι) → ι) → (ι → ι → ι) → ι) → ι . ∀ x2 : (ι → ι) → ι → ι . ∀ x3 : (((((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι) → ι → ι → ι → ι → ι) → ι → ι . (∀ x4 : (((ι → ι) → ι → ι) → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : (((ι → ι) → ι → ι) → ι → ι → ι) → ι → (ι → ι) → ι . ∀ x7 . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x10 x11 x12 x13 . Inj1 (x1 (λ x14 . 0) (λ x14 : ((ι → ι) → ι) → ι . λ x15 : ι → ι → ι . 0))) (x0 (λ x9 . x6 (λ x10 : (ι → ι) → ι → ι . λ x11 x12 . Inj0 (x2 (λ x13 . 0) 0)) 0 (λ x10 . Inj1 (Inj0 0))) (λ x9 : (ι → ι) → ι . x5)) = setsum 0 x5) ⟶ (∀ x4 . ∀ x5 : (((ι → ι) → ι → ι) → (ι → ι) → ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x10 x11 x12 x13 . x10) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x2 (λ x12 . 0) (x7 (x7 0))) (setsum x6 (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x10 x11 x12 x13 . x12) (setsum 0 0))) (setsum (x7 (x3 (λ x9 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x10 x11 x12 x13 . 0) 0)) (x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . x0 (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0)) 0 (x7 0)))) = x5 (λ x9 : (ι → ι) → ι → ι . λ x10 : ι → ι . λ x11 . Inj0 0) (Inj0 0) (x1 (λ x9 . x6) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . setsum (x2 (λ x11 . Inj1 0) (setsum 0 0)) (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x12 x13 x14 x15 . x13) (x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)))))) ⟶ (∀ x4 : ι → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 . ∀ x6 : ι → ι . ∀ x7 . x2 (λ x9 . x2 (λ x10 . x0 (λ x11 . 0) (λ x11 : (ι → ι) → ι . 0)) (x1 (λ x10 . Inj1 x7) (λ x10 : ((ι → ι) → ι) → ι . λ x11 : ι → ι → ι . x1 (λ x12 . Inj1 0) (λ x12 : ((ι → ι) → ι) → ι . λ x13 : ι → ι → ι . 0)))) (setsum (x2 (λ x9 . x7) 0) (Inj1 (Inj0 (x4 0 (λ x9 x10 . 0) (λ x9 . 0))))) = setsum x7 0) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x6 x7 . x2 (λ x9 . Inj0 x7) 0 = x4 (λ x9 : ι → ι → ι . x9 x6 (x2 (λ x10 . setsum x6 0) 0)) (λ x9 : ι → ι . λ x10 . 0) 0 (x0 (λ x9 . x7) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x11 x12 x13 x14 . 0) 0))) ⟶ (∀ x4 : (((ι → ι) → ι) → ι → ι → ι) → (ι → ι) → ι → ι . ∀ x5 : ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 : ι → ((ι → ι) → ι) → ι . x1 (λ x9 . Inj0 (x6 (λ x10 : (ι → ι) → ι → ι . setsum (setsum 0 0) (setsum 0 0)))) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . setsum (Inj1 0) (x0 (λ x11 . x3 (λ x12 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x13 x14 x15 x16 . x2 (λ x17 . 0) 0) 0) (λ x11 : (ι → ι) → ι . x11 (λ x12 . x3 (λ x13 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x14 x15 x16 x17 . 0) 0)))) = Inj0 (x7 (setsum (x0 (λ x9 . Inj1 0) (λ x9 : (ι → ι) → ι . x3 (λ x10 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x11 x12 x13 x14 . 0) 0)) (setsum (Inj1 0) (setsum 0 0))) (λ x9 : ι → ι . x7 (x5 (x5 0)) (λ x10 : ι → ι . 0)))) ⟶ (∀ x4 . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . setsum (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x12 x13 x14 x15 . 0) (x7 (Inj0 0))) (Inj1 (setsum 0 (x3 (λ x11 : (((ι → ι) → ι → ι) → ι) → ((ι → ι) → ι) → ι . λ x12 x13 x14 x15 . 0) 0)))) = setsum (x5 (λ x9 x10 x11 . x9)) (x1 (λ x9 . 0) (λ x9 : ((ι → ι) → ι) → ι . λ x10 : ι → ι → ι . x1 (λ x11 . x0 (λ x12 . 0) (λ x12 : (ι → ι) → ι . 0)) (λ x11 : ((ι → ι) → ι) → ι . λ x12 : ι → ι → ι . Inj1 0)))) ⟶ (∀ x4 x5 . ∀ x6 : (ι → (ι → ι) → ι) → ι . ∀ x7 : (ι → ι) → ι . x0 (λ x9 . 0) (λ x9 : (ι → ι) → ι . x7 (λ x10 . x10)) = Inj0 (x0 (λ x9 . 0) (λ x9 : (ι → ι) → ι . 0))) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x0 (λ x9 . x2 (λ x10 . 0) 0) (λ x9 : (ι → ι) → ι . 0) = x2 (λ x9 . Inj0 (setsum (Inj0 x9) 0)) (Inj0 0)) ⟶ False (proof)
Theorem 55e40.. : ∀ x0 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x1 : ((((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 → ι) → ι → ι) → ι → ι → ι . ∀ x3 : (ι → (ι → ι) → ι) → ι → ι . (∀ x4 : ι → ((ι → ι) → ι → ι) → ι → ι → ι . ∀ x5 : ι → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 : (ι → (ι → ι) → ι → ι) → ι . x3 (λ x9 . λ x10 : ι → ι . Inj1 (Inj0 0)) (Inj0 (x7 (λ x9 . λ x10 : ι → ι . λ x11 . x10 (setsum 0 0)))) = x6 (λ x9 . x0 (λ x10 . x6 (x3 (λ x11 . λ x12 : ι → ι . x0 (λ x13 . 0) (λ x13 : ι → ι . 0)))) (λ x10 : ι → ι . x7 (λ x11 . λ x12 : ι → ι . λ x13 . x10 (x3 (λ x14 . λ x15 : ι → ι . 0) 0))))) ⟶ (∀ x4 x5 . ∀ x6 : ι → ((ι → ι) → ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x3 (λ x9 . λ x10 : ι → ι . x10 0) x5 = setsum (x7 (λ x9 . x7 (λ x10 . Inj1 x9))) (Inj0 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : ι → (ι → ι → ι) → ι → ι . ∀ x7 : ι → (ι → ι) → (ι → ι) → ι . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x2 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . x16 (Inj0 (x17 0)) 0) (x0 (λ x14 . 0) (λ x14 : ι → ι . 0)) (x1 (λ x14 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x15 . Inj1 (x14 (λ x16 : ι → ι → ι . λ x17 . 0) 0)) 0 0 (λ x14 . setsum (x2 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 0) (x3 (λ x15 . λ x16 : ι → ι . 0) 0)) (λ x14 . x12 (setsum 0 0)))) (x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . Inj0 0) (x7 (x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . 0) 0 (setsum 0 0) (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0 0) (λ x9 . 0)) (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x3 (λ x15 . λ x16 : ι → ι . 0) 0) (x1 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x11 . 0) 0 0 (λ x10 . 0) (λ x10 . 0)) 0) (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . setsum 0 0) x9 0)) 0 (λ x9 . x6 (setsum (x0 (λ x10 . 0) (λ x10 : ι → ι . 0)) (Inj0 0)) (λ x10 x11 . 0) (x6 (x1 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x11 . 0) 0 0 (λ x10 . 0) (λ x10 . 0)) (λ x10 x11 . x1 (λ x12 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x13 . 0) 0 0 (λ x12 . 0) (λ x12 . 0)) (setsum 0 0))) (λ x9 . x9)) (setsum 0 (x4 0)) = setsum (x0 (λ x9 . x3 (λ x10 . λ x11 : ι → ι . x9) (x7 (x7 0 (λ x10 . 0) (λ x10 . 0)) (λ x10 . x0 (λ x11 . 0) (λ x11 : ι → ι . 0)) (λ x10 . 0))) (λ x9 : ι → ι . x5)) (x4 (x3 (λ x9 . λ x10 : ι → ι . setsum (Inj1 0) (setsum 0 0)) (x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . 0) x5 0 (λ x9 . Inj1 0) (λ x9 . x1 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x11 . 0) 0 0 (λ x10 . 0) (λ x10 . 0)))))) ⟶ (∀ x4 : ι → ((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 x7 . x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x1 (λ x14 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x15 . x0 (λ x16 . x14 (λ x17 : ι → ι → ι . λ x18 . Inj1 0) x15) (λ x16 : ι → ι . Inj1 0)) (setsum 0 (x10 (λ x14 : ι → ι . λ x15 . x15) (λ x14 . 0))) 0 (λ x14 . x0 (λ x15 . setsum 0 (setsum 0 0)) (λ x15 : ι → ι . x2 (λ x16 : ι → ι . λ x17 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x18 : ι → ι → ι . λ x19 : ι → ι . λ x20 . x3 (λ x21 . λ x22 : ι → ι . 0) 0) (x12 0) 0)) (λ x14 . x14)) 0 (Inj1 0) = x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . setsum (setsum (Inj1 (x1 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x12 . 0) 0 0 (λ x11 . 0) (λ x11 . 0))) (x9 (λ x11 : ι → ι → ι . λ x12 . 0) (Inj1 0))) x6) (Inj1 (Inj1 0)) (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x13) (x4 (setsum (x3 (λ x9 . λ x10 : ι → ι . 0) 0) (x0 (λ x9 . 0) (λ x9 : ι → ι . 0))) (λ x9 : ι → ι . x0 (λ x10 . setsum 0 0) (λ x10 : ι → ι . Inj1 0))) (x5 (setsum (x3 (λ x9 . λ x10 : ι → ι . 0) 0) (x4 0 (λ x9 : ι → ι . 0))))) (λ x9 . Inj0 (setsum (setsum (Inj0 0) (Inj1 0)) (x3 (λ x10 . λ x11 : ι → ι . 0) 0))) (λ x9 . setsum 0 x6)) ⟶ (∀ x4 : ((ι → ι → ι) → ι) → ι → ι → ι . ∀ x5 : (ι → ι → ι → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . Inj1 0) (x5 (λ x9 x10 x11 . x3 (λ x12 . λ x13 : ι → ι . setsum (x2 (λ x14 : ι → ι . λ x15 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x16 : ι → ι → ι . λ x17 : ι → ι . λ x18 . 0) 0 0) 0) 0)) 0 (λ x9 . x3 (λ x10 . λ x11 : ι → ι . x9) 0) (λ x9 . 0) = x5 (λ x9 x10 x11 . setsum x9 (x1 (λ x12 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x13 . x0 (λ x14 . x2 (λ x15 : ι → ι . λ x16 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x17 : ι → ι → ι . λ x18 : ι → ι . λ x19 . 0) 0 0) (λ x14 : ι → ι . Inj0 0)) x9 0 (λ x12 . x10) (λ x12 . 0)))) ⟶ (∀ x4 : ι → ι . ∀ x5 : (ι → ι → ι) → ι → ι . ∀ x6 : (((ι → ι) → ι) → (ι → ι) → ι) → ((ι → ι) → ι) → (ι → ι) → ι . ∀ x7 . x1 (λ x9 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x10 . Inj0 (setsum (x1 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x12 . 0) (x3 (λ x11 . λ x12 : ι → ι . 0) 0) (x1 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x12 . 0) 0 0 (λ x11 . 0) (λ x11 . 0)) (λ x11 . 0) (λ x11 . x10)) 0)) 0 (Inj1 (x5 (λ x9 x10 . Inj1 0) 0)) (λ x9 . 0) (λ x9 . setsum x9 (x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x12 x14 0) 0 0)) = Inj1 (Inj0 (Inj0 0))) ⟶ (∀ x4 : ι → ι . ∀ x5 . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 . x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . x0 (λ x15 . 0) (λ x15 : ι → ι . 0)) (x1 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x11 . x9) (x1 (λ x10 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x11 . Inj0 0) (x2 (λ x10 : ι → ι . λ x11 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x12 : ι → ι → ι . λ x13 : ι → ι . λ x14 . 0) 0 0) x7 (λ x10 . x9) (λ x10 . x1 (λ x11 : ((ι → ι → ι) → ι → ι) → ι → ι . λ x12 . 0) 0 0 (λ x11 . 0) (λ x11 . 0))) (x0 (λ x10 . Inj0 0) (λ x10 : ι → ι . 0)) (λ x10 . 0) (λ x10 . Inj1 (Inj0 0))) (setsum (setsum (setsum 0 0) (Inj1 0)) (Inj0 0))) (λ x9 : ι → ι . x5) = setsum (setsum (x4 (x3 (λ x9 . λ x10 : ι → ι . x0 (λ x11 . 0) (λ x11 : ι → ι . 0)) (x0 (λ x9 . 0) (λ x9 : ι → ι . 0)))) (setsum (Inj1 (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0)) 0)) (Inj1 (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x12 (x3 (λ x14 . λ x15 : ι → ι . 0) 0)) (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . x3 (λ x14 . λ x15 : ι → ι . 0) 0) 0 0) (Inj0 (x4 0))))) ⟶ (∀ x4 . ∀ x5 : ((ι → ι) → ι) → ι → (ι → ι) → ι → ι . ∀ x6 x7 . x0 Inj1 (λ x9 : ι → ι . x6) = setsum (x2 (λ x9 : ι → ι . λ x10 : ((ι → ι) → ι → ι) → (ι → ι) → ι . λ x11 : ι → ι → ι . λ x12 : ι → ι . λ x13 . 0) 0 0) 0) ⟶ False (proof)
Theorem d1c2c.. : ∀ 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) → ι) → ι → ι) → ι → ι . (∀ x4 : ι → ι . ∀ x5 x6 x7 . x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . x3 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x16 . λ x17 : (ι → ι → ι) → ι . λ x18 . x0 (λ x19 . λ x20 : (ι → ι → ι) → ι . 0) 0) x12) x11 (x3 (λ x15 . λ x16 : (ι → ι → ι) → ι . λ x17 . x2 (λ x18 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (x0 (λ x15 . λ x16 : (ι → ι → ι) → ι . 0) 0))) 0) 0 = x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . x1 (λ x14 : ι → ι . x13 (λ x15 x16 . x0 (λ x17 . λ x18 : (ι → ι → ι) → ι . 0) 0)) (λ x14 x15 . λ x16 : ι → ι . λ x17 . 0) (Inj0 (x3 (λ x14 . λ x15 : (ι → ι → ι) → ι . λ x16 . 0) 0)) (λ x14 x15 . setsum (x2 (λ x16 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (Inj1 0)) (λ x14 . 0) 0) (x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . x2 (λ x14 : (ι → ι) → (ι → ι → ι) → ι → ι . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (setsum 0 0) (x10 (λ x14 x15 . 0))) x9)) (Inj1 (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . 0) x6))) ⟶ (∀ x4 x5 . ∀ x6 : ((ι → ι) → ι → ι → ι) → ι . ∀ x7 : ι → (ι → ι → ι) → ι . x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . x9) 0 = x4) ⟶ (∀ x4 x5 x6 . ∀ x7 : (ι → ι) → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . setsum (x1 (λ x10 : ι → ι . setsum 0 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . x0 (λ x14 . λ x15 : (ι → ι → ι) → ι . 0) 0) (x7 (λ x10 . 0)) (λ x10 x11 . x10) (λ x10 . setsum 0 0) (Inj1 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι → ι . Inj1 0) (Inj1 0) (x9 (λ x10 . 0) (λ x10 x11 . 0) 0))) 0 (x1 (λ x9 : ι → ι . x6) (λ x9 x10 . λ x11 : ι → ι . λ x12 . setsum (Inj0 0) (setsum 0 0)) (Inj1 (x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . 0) 0)) (λ x9 x10 . 0) (λ x9 . 0) (setsum x5 (x1 (λ x9 : ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) 0 (λ x9 x10 . 0) (λ x9 . 0) 0)))) 0 = x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . x1 (λ x10 : ι → ι . x6) (λ x10 x11 . λ x12 : ι → ι . λ x13 . Inj0 0) 0 (λ x10 x11 . 0) (λ x10 . x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . 0) (setsum 0 (x1 (λ x11 : ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) 0 (λ x11 x12 . 0) (λ x11 . 0) 0))) (setsum 0 x5)) (Inj0 0) (Inj1 (x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . 0) 0) (Inj0 (x1 (λ x9 : ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . 0) 0 (λ x9 x10 . 0) (λ x9 . 0) 0))))) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 : (((ι → ι) → ι → ι) → ι) → (ι → ι → ι) → ι → ι → ι . ∀ x6 . ∀ x7 : ((ι → ι → ι) → ι → ι) → ι → ι . x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (x1 (λ x9 : ι → ι . setsum (Inj0 0) (x7 (λ x10 : ι → ι → ι . λ x11 . 0) 0)) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x9) (setsum (setsum (x5 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0 0) (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . 0) 0)) 0) (λ x9 x10 . x0 (λ x11 . λ x12 : (ι → ι → ι) → ι . x9) (Inj1 x10)) (λ x9 . x9) (x7 (λ x9 : ι → ι → ι . λ x10 . 0) (Inj1 (x5 (λ x9 : (ι → ι) → ι → ι . 0) (λ x9 x10 . 0) 0 0)))) (x1 (λ x9 : ι → ι . 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x0 (λ x13 . λ x14 : (ι → ι → ι) → ι . 0) (x11 (x3 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 . 0) 0))) (x7 (λ x9 : ι → ι → ι . λ x10 . 0) (Inj0 (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0))) (λ x9 x10 . setsum x9 0) (λ x9 . setsum (Inj0 x9) (setsum x9 (x3 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . 0) 0))) 0) = Inj1 0) ⟶ (∀ x4 : ((ι → ι) → ι) → (ι → ι → ι) → (ι → ι) → ι . ∀ x5 : ι → ι → ι → ι . ∀ x6 : (((ι → ι) → ι → ι) → ι) → ι . ∀ x7 . x1 (λ x9 : ι → ι . x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . setsum 0 (Inj0 0)) (x9 0)) (Inj1 (x6 (λ x10 : (ι → ι) → ι → ι . Inj1 0))) (setsum (x5 0 (x5 0 0 0) 0) (Inj1 0))) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x9) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . x0 (λ x13 . λ x14 : (ι → ι → ι) → ι . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (setsum 0 0)) 0) 0 0) (λ x9 x10 . x1 (λ x11 : ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x2 (λ x15 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (setsum (x0 (λ x15 . λ x16 : (ι → ι → ι) → ι . 0) 0) x14) 0) (x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . setsum (Inj1 0) 0) (Inj1 0)) (λ x11 x12 . 0) (λ x11 . x1 (λ x12 : ι → ι . setsum 0 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . setsum (Inj0 0) (setsum 0 0)) (Inj0 0) (λ x12 x13 . x11) (λ x12 . x11) 0) (x1 (λ x11 : ι → ι . x11 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . Inj0 0) (x6 (λ x11 : (ι → ι) → ι → ι . setsum 0 0)) (λ x11 x12 . x11) (λ x11 . setsum x9 (x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . 0) 0)) (Inj1 (setsum 0 0)))) (λ x9 . Inj1 (setsum x9 (x1 (λ x10 : ι → ι . Inj1 0) (λ x10 x11 . λ x12 : ι → ι . λ x13 . setsum 0 0) (x3 (λ x10 . λ x11 : (ι → ι → ι) → ι . λ x12 . 0) 0) (λ x10 x11 . x3 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 . 0) 0) (λ x10 . 0) 0))) (setsum 0 (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι → ι . x1 (λ x12 : ι → ι . 0) (λ x12 x13 . λ x14 : ι → ι . λ x15 . 0) 0 (λ x12 x13 . 0) (λ x12 . 0) 0) (x6 (λ x11 : (ι → ι) → ι → ι . 0)) (x0 (λ x11 . λ x12 : (ι → ι → ι) → ι . 0) 0)) 0)) = x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . setsum (Inj1 0) (x9 (λ x10 . x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (x1 (λ x11 : ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) 0 (λ x11 x12 . 0) (λ x11 . 0) 0) (Inj1 0)) (λ x10 x11 . x3 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 . Inj1 0) (setsum 0 0)) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 (setsum 0 0)))) (Inj1 0) (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . x3 (λ x11 . λ x12 : (ι → ι → ι) → ι . λ x13 . x11) (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) x7 (setsum 0 0))) 0)) ⟶ (∀ x4 : (ι → (ι → ι) → ι) → ι . ∀ x5 . ∀ x6 : ι → ι → ι → ι → ι . ∀ x7 . x1 (λ x9 : ι → ι . x6 (Inj0 (x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . setsum 0 0) (x9 0))) (x2 (λ x10 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) (Inj0 (x0 (λ x10 . λ x11 : (ι → ι → ι) → ι . 0) 0)) (setsum 0 0)) 0 0) (λ x9 x10 . λ x11 : ι → ι . λ x12 . Inj1 0) (x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . setsum 0 0) (x6 x5 x7 0 (x1 (λ x9 : ι → ι . x7) (λ x9 x10 . λ x11 : ι → ι . λ x12 . x2 (λ x13 : (ι → ι) → (ι → ι → ι) → ι → ι . 0) 0 0) (x4 (λ x9 . λ x10 : ι → ι . 0)) (λ x9 x10 . x6 0 0 0 0) (λ x9 . x9) (x6 0 0 0 0)))) (λ x9 . x1 (λ x10 : ι → ι . setsum 0 (Inj1 0)) (λ x10 x11 . λ x12 : ι → ι . Inj0) 0 (λ x10 . x1 (λ x11 : ι → ι . setsum (x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . 0) 0) (x0 (λ x12 . λ x13 : (ι → ι → ι) → ι . 0) 0)) (λ x11 x12 . λ x13 : ι → ι . x3 (λ x14 . λ x15 : (ι → ι → ι) → ι . λ x16 . 0)) x9 (λ x11 x12 . 0) (λ x11 . 0)) (λ x10 . setsum x9 (x1 (λ x11 : ι → ι . x9) (λ x11 x12 . λ x13 : ι → ι . λ x14 . x13 0) (Inj0 0) (λ x11 x12 . x3 (λ x13 . λ x14 : (ι → ι → ι) → ι . λ x15 . 0) 0) (λ x11 . x10) 0))) (λ x9 . 0) 0 = Inj0 (Inj1 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . x9) (x2 (λ x9 : (ι → ι) → (ι → ι → ι) → ι → ι . setsum (setsum x6 0) (setsum 0 (setsum 0 0))) (x5 x6 (Inj1 0)) (x4 (setsum (Inj0 0) x7))) = setsum 0 (x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . setsum (setsum (x0 (λ x11 . λ x12 : (ι → ι → ι) → ι . 0) 0) (x1 (λ x11 : ι → ι . 0) (λ x11 x12 . λ x13 : ι → ι . λ x14 . 0) 0 (λ x11 x12 . 0) (λ x11 . 0) 0)) (x2 (λ x11 : (ι → ι) → (ι → ι → ι) → ι → ι . x3 (λ x12 . λ x13 : (ι → ι → ι) → ι . λ x14 . 0) 0) 0 (Inj0 0))) 0)) ⟶ (∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι) → ι . ∀ x7 . x0 (λ x9 . λ x10 : (ι → ι → ι) → ι . x7) (x3 (λ x9 . λ x10 : (ι → ι → ι) → ι . λ x11 . Inj0 0) x4) = x7) ⟶ False (proof)

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