Proofgold Proof

pf
Let x0 of type ι be given. Let x1 of type ι be given. Let x2 of type ι be given. Assume H0: SNo x0. Assume H1: ∀ x3 . x3 ∈ SNoS_ (SNoLev x0) ⟶ add_SNo x3 x1 = add_SNo x1 x3. Assume H2: SNo x2. The subproof is completed by applying H1 with x2. ■