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Proofgold Proposition

∀ x0 : (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)(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 . ∀ x6 x7 . x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 x11 x12 . x1 (λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . setsum 0 0) (λ x13 : ι → (ι → ι)ι → ι . λ x14 x15 . x15)) = x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . x9 (x11 (Inj1 (Inj1 0))) (x10 (x0 (λ x12 . 0) (setsum 0 0))) 0) (λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . Inj1 0))(∀ x4 : (ι → (ι → ι)ι → ι)((ι → ι) → ι) → ι . ∀ x5 : ι → ι . ∀ x6 . ∀ x7 : ι → ι . x3 Inj0 (λ x9 : ι → ι . λ x10 x11 x12 . x12) = setsum 0 (x4 (λ x9 . λ x10 : ι → ι . λ x11 . setsum (setsum (x1 (λ x12 : ι → ι → ι → ι . λ x13 x14 : ι → ι . 0) (λ x12 : ι → (ι → ι)ι → ι . λ x13 x14 . 0)) x11) (x10 (x2 (λ x12 : (ι → ι → ι) → ι . λ x13 : ι → ι . λ x14 : (ι → ι) → ι . 0) (λ x12 x13 x14 x15 . 0) (λ x12 : (ι → ι)ι → ι . 0)))) (λ x9 : ι → ι . x5 0)))(∀ x4 . ∀ x5 : ι → ι . ∀ x6 : (ι → ι)ι → ι . ∀ x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . Inj0 (setsum 0 0)) (λ x9 x10 x11 x12 . Inj1 0) (λ x9 : (ι → ι)ι → ι . x1 (λ x10 : ι → ι → ι → ι . λ x11 x12 : ι → ι . Inj0 (Inj0 (x12 0))) (λ x10 : ι → (ι → ι)ι → ι . λ x11 x12 . Inj1 (x0 (λ x13 . 0) (x1 (λ x13 : ι → ι → ι → ι . λ x14 x15 : ι → ι . 0) (λ x13 : ι → (ι → ι)ι → ι . λ x14 x15 . 0))))) = Inj0 0)(∀ x4 : ((ι → ι)(ι → ι)ι → ι) → ι . ∀ x5 : ((ι → ι → ι) → ι) → ι . ∀ x6 x7 . x2 (λ x9 : (ι → ι → ι) → ι . λ x10 : ι → ι . λ x11 : (ι → ι) → ι . x7) (λ x9 x10 x11 x12 . x12) (λ x9 : (ι → ι)ι → ι . 0) = x7)(∀ x4 . ∀ x5 : ((ι → ι → ι)(ι → ι)ι → ι) → ι . ∀ x6 : ((ι → ι) → ι)ι → (ι → ι) → ι . ∀ x7 : (ι → ι) → ι . x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . x11 0) (λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . x11) = x5 (λ x9 : ι → ι → ι . λ x10 : ι → ι . λ x11 . x10 (x10 (x0 (λ x12 . x0 (λ x13 . 0) 0) 0))))(∀ x4 . ∀ x5 : (((ι → ι) → ι) → ι) → ι . ∀ x6 . ∀ x7 : ι → ι . x1 (λ x9 : ι → ι → ι → ι . λ x10 x11 : ι → ι . 0) (λ x9 : ι → (ι → ι)ι → ι . λ x10 x11 . setsum x11 (x9 x11 (λ x12 . setsum (setsum 0 0) 0) (x0 (λ x12 . 0) x10))) = setsum 0 (x3 (λ x9 . 0) (λ x9 : ι → ι . λ x10 x11 x12 . Inj0 (x9 x11))))(∀ x4 x5 . ∀ x6 : (((ι → ι)ι → ι)ι → ι)ι → ι → ι → ι . ∀ x7 : ι → (ι → ι → ι)ι → ι → ι . x0 (λ x9 . 0) 0 = x4)(∀ x4 . ∀ x5 : ι → ι . ∀ x6 : ι → ((ι → ι) → ι)ι → ι . ∀ x7 : ι → ι . x0 (λ x9 . x5 (x0 (λ x10 . x3 (λ x11 . Inj0 0) (λ x11 : ι → ι . λ x12 x13 x14 . x11 0)) (x0 (λ x10 . x9) (x0 (λ x10 . 0) 0)))) 0 = Inj1 (x3 (λ x9 . x2 (λ x10 : (ι → ι → ι) → ι . λ x11 : ι → ι . λ x12 : (ι → ι) → ι . 0) (λ x10 x11 x12 x13 . x13) (λ x10 : (ι → ι)ι → ι . Inj1 (Inj0 0))) (λ x9 : ι → ι . λ x10 x11 x12 . x9 (x0 (λ x13 . Inj1 0) (Inj1 0)))))False
type
prop
theory
HF
name
-
proof
PURws..
Megalodon
-
proofgold address
TMMrF..
creator
11849 PrGVS../06efe..
owner
11889 PrGVS../92eba..
term root
2c06c..