Let x be given.

Assume Hx.

Apply SNoLev_prop x Hx to the current goal.

Assume Hx1: ordinal (SNoLev x).

Assume Hx2: SNo_ (SNoLev x) x.

Apply SNo_PSNo_eta_ to the current goal.

We will prove ordinal (SNoLev x).

An exact proof term for the current goal is Hx1.

We will prove SNo_ (SNoLev x) x.

An exact proof term for the current goal is Hx2.

∎