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Proofgold Proof

pf
Apply unknownprop_50f1b502ede8f73efac5f5638826e50355eb6f972374cae79b4ecf4e1be40675 with ∀ x0 : (ι → (ι → ι) → ι) → ((ι → (ι → ι) → ι) → ι) → ο . ∀ x1 : (ι → (ι → ι) → ι → ι → ι) → ((ι → (ι → ι) → ι → ι) → ι → ι → ι → ι) → (((ι → ι) → ι) → ι) → ο . ∀ x2 : ((ι → ι) → ι → ι) → (ι → ((ι → ι) → ι → ι) → ι) → ο . ∀ x3 : ((((ι → ι) → ι) → ι → ι) → ι) → ι → ο . (∀ x4 : ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . setsum 0 x5) ⟶ x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj1 0) x6) (setsum (Inj0 0) (setsum (Inj1 (x4 0)) (Inj1 (Inj0 0))))) ⟶ (∀ x4 : (((ι → ι) → ι) → (ι → ι) → ι → ι) → ι . ∀ x5 : ι → (ι → ι) → ι → ι . ∀ x6 : ι → ((ι → ι) → ι) → ι → ι . ∀ x7 . x3 (λ x8 : ((ι → ι) → ι) → ι → ι . x8 (λ x9 : ι → ι . Inj0 x7) 0) (Inj1 x7) ⟶ False) ⟶ (∀ x4 . ∀ x5 : (ι → ι) → ((ι → ι) → ι) → ι . ∀ x6 : (ι → ι → ι) → ι . ∀ x7 . x2 (λ x8 : ι → ι . λ x9 . setsum (x8 (setsum 0 (setsum 0 0))) x7) (λ x8 . λ x9 : (ι → ι) → ι → ι . x6 (λ x10 x11 . setsum (setsum x11 (setsum 0 0)) x11)) ⟶ x2 (λ x8 : ι → ι . λ x9 . 0) (λ x8 . λ x9 : (ι → ι) → ι → ι . Inj1 (Inj1 0))) ⟶ (∀ x4 : (ι → ι) → ι . ∀ x5 x6 x7 . x2 (λ x8 : ι → ι . λ x9 . Inj1 x9) (λ x8 . λ x9 : (ι → ι) → ι → ι . 0) ⟶ False) ⟶ (∀ x4 : ι → ι → ι → ι → ι . ∀ x5 x6 . ∀ x7 : ι → ι . In (Inj1 0) (setsum (Inj0 (x4 (setsum 0 0) (Inj1 0) (Inj1 0) (setsum 0 0))) 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj1 (setsum 0 (Inj1 0))) (x9 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . x11) (λ x8 : (ι → ι) → ι . 0) ⟶ x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . 0) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . setsum (setsum 0 (Inj0 0)) (setsum (Inj0 0) 0)) (λ x8 : (ι → ι) → ι . setsum (Inj0 (x7 (setsum 0 0))) 0)) ⟶ (∀ x4 : ι → ι . ∀ x5 x6 x7 . x1 (λ x8 . λ x9 : ι → ι . λ x10 x11 . setsum (Inj0 (setsum (setsum 0 0) (Inj0 0))) (setsum (setsum (setsum 0 0) 0) (Inj1 0))) (λ x8 : ι → (ι → ι) → ι → ι . λ x9 x10 x11 . 0) (λ x8 : (ι → ι) → ι . setsum 0 (Inj0 x6)) ⟶ In (Inj1 (Inj1 0)) x7) ⟶ (∀ x4 x5 : ι → ι → ι . ∀ x6 x7 . x0 (λ x8 . λ x9 : ι → ι . 0) (λ x8 : ι → (ι → ι) → ι . x7) ⟶ x0 (λ x8 . λ x9 : ι → ι . x6) (λ x8 : ι → (ι → ι) → ι . 0)) ⟶ (∀ x4 : ι → ι → ι . ∀ x5 . ∀ x6 x7 : ι → ι . x0 (λ x8 . λ x9 : ι → ι . Inj0 (setsum 0 (Inj1 0))) (λ x8 : ι → (ι → ι) → ι . 0) ⟶ In (setsum 0 0) (Inj0 0)) ⟶ False.
The subproof is completed by applying unknownprop_7a61a2e26325a5359038b4e35ad92a6b0df32826755135948912b2230c25ba52.
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