Let α be given.
Assume Ha.
Let x be given.
Assume Hx: SNo_ α x.
We prove the intermediate claim Lx: SNo x.
An exact proof term for the current goal is SNo_SNo α Ha x Hx.
We prove the intermediate claim Lxa: SNoLev x = α.
An exact proof term for the current goal is SNoLev_uniq2 α Ha x Hx.
We prove the intermediate claim Lmxa: SNoLev (- x) = α.
rewrite the current goal using minus_SNo_Lev x Lx (from left to right).
An exact proof term for the current goal is Lxa.
We will prove SNo_ α (- x).
rewrite the current goal using Lmxa (from right to left).
We will prove SNo_ (SNoLev (- x)) (- x).
Apply SNoLev_ to the current goal.
We will prove SNo (- x).
An exact proof term for the current goal is SNo_minus_SNo x Lx.