Proofgold Proposition

∀ x0 : ι → ι → ι . (∀ x1 x2 . SNo x1 ⟶ SNo x2 ⟶ SNo (x0 x1 x2)) ⟶ (∀ x1 x2 x3 . SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ x0 x1 (add_SNo x2 x3) = add_SNo (x0 x1 x2) (x0 x1 x3)) ⟶ (∀ x1 x2 x3 . SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ x0 (add_SNo x1 x2) x3 = add_SNo (x0 x1 x3) (x0 x2 x3)) ⟶ (∀ x1 x2 . SNo x1 ⟶ SNo x2 ⟶ ∀ x3 . x3 ∈ SNoL (x0 x1 x2) ⟶ ∀ x4 : ο . (∀ x5 . x5 ∈ SNoL x1 ⟶ ∀ x6 . x6 ∈ SNoL x2 ⟶ SNoLe (add_SNo x3 (x0 x5 x6)) (add_SNo (x0 x5 x2) (x0 x1 x6)) ⟶ x4) ⟶ (∀ x5 . x5 ∈ SNoR x1 ⟶ ∀ x6 . x6 ∈ SNoR x2 ⟶ SNoLe (add_SNo x3 (x0 x5 x6)) (add_SNo (x0 x5 x2) (x0 x1 x6)) ⟶ x4) ⟶ x4) ⟶ (∀ x1 x2 . SNo x1 ⟶ SNo x2 ⟶ ∀ x3 . x3 ∈ SNoR (x0 x1 x2) ⟶ ∀ x4 : ο . (∀ x5 . x5 ∈ SNoL x1 ⟶ ∀ x6 . x6 ∈ SNoR x2 ⟶ SNoLe (add_SNo (x0 x5 x2) (x0 x1 x6)) (add_SNo x3 (x0 x5 x6)) ⟶ x4) ⟶ (∀ x5 . x5 ∈ SNoR x1 ⟶ ∀ x6 . x6 ∈ SNoL x2 ⟶ SNoLe (add_SNo (x0 x5 x2) (x0 x1 x6)) (add_SNo x3 (x0 x5 x6)) ⟶ x4) ⟶ x4) ⟶ (∀ x1 x2 x3 x4 . SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNoLt x3 x1 ⟶ SNoLt x4 x2 ⟶ SNoLt (add_SNo (x0 x3 x2) (x0 x1 x4)) (add_SNo (x0 x1 x2) (x0 x3 x4))) ⟶ (∀ x1 x2 x3 x4 . SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ SNo x4 ⟶ SNoLe x3 x1 ⟶ SNoLe x4 x2 ⟶ SNoLe (add_SNo (x0 x3 x2) (x0 x1 x4)) (add_SNo (x0 x1 x2) (x0 x3 x4))) ⟶ ∀ x1 x2 x3 . SNo x1 ⟶ SNo x2 ⟶ SNo x3 ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x1) ⟶ x0 x4 (x0 x2 x3) = x0 (x0 x4 x2) x3) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x2) ⟶ x0 x1 (x0 x4 x3) = x0 (x0 x1 x4) x3) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x3) ⟶ x0 x1 (x0 x2 x4) = x0 (x0 x1 x2) x4) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x1) ⟶ ∀ x5 . x5 ∈ SNoS_ (SNoLev x2) ⟶ x0 x4 (x0 x5 x3) = x0 (x0 x4 x5) x3) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x1) ⟶ ∀ x5 . x5 ∈ SNoS_ (SNoLev x3) ⟶ x0 x4 (x0 x2 x5) = x0 (x0 x4 x2) x5) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x2) ⟶ ∀ x5 . x5 ∈ SNoS_ (SNoLev x3) ⟶ x0 x1 (x0 x4 x5) = x0 (x0 x1 x4) x5) ⟶ (∀ x4 . x4 ∈ SNoS_ (SNoLev x1) ⟶ ∀ x5 . x5 ∈ SNoS_ (SNoLev x2) ⟶ ∀ x6 . x6 ∈ SNoS_ (SNoLev x3) ⟶ x0 x4 (x0 x5 x6) = x0 (x0 x4 x5) x6) ⟶ ∀ x4 . (∀ x5 . x5 ∈ x4 ⟶ ∀ x6 : ο . (∀ x7 . x7 ∈ SNoL x1 ⟶ ∀ x8 . x8 ∈ SNoL (x0 x2 x3) ⟶ x5 = add_SNo (x0 x7 (x0 x2 x3)) (add_SNo (x0 x1 x8) (minus_SNo (x0 x7 x8))) ⟶ x6) ⟶ (∀ x7 . x7 ∈ SNoR x1 ⟶ ∀ x8 . x8 ∈ SNoR (x0 x2 x3) ⟶ x5 = add_SNo (x0 x7 (x0 x2 x3)) (add_SNo (x0 x1 x8) (minus_SNo (x0 x7 x8))) ⟶ x6) ⟶ x6) ⟶ ∀ x5 . x5 ∈ x4 ⟶ SNoLt x5 (x0 (x0 x1 x2) x3)

type
prop

theory
HotG

name
mul_SNo_assoc_lem1

proof
PUVtn..

Megalodon
mul_SNo_assoc_lem1

proofgold address
TMXsW..^{mul_SNo_assoc_lem1}

creator
5161 Pr6Pc../52bf4..

owner
5161 Pr6Pc../52bf4..

term root
fca03..