Apply Empty_Subq_eq with
SNoR 0.
Let x0 of type ι be given.
Assume H0:
x0 ∈ SNoR 0.
Claim L1:
x0 ∈ SNoS_ 0
Apply SNoLev_0 with
λ x1 x2 . x0 ∈ SNoS_ x1.
Apply SNoR_SNoS_ with
0,
x0.
The subproof is completed by applying H0.
Apply SNoS_E2 with
0,
x0,
x0 ∈ 0 leaving 3 subgoals.
The subproof is completed by applying ordinal_Empty.
The subproof is completed by applying L1.
Apply FalseE with
ordinal (SNoLev x0) ⟶ SNo x0 ⟶ SNo_ (SNoLev x0) x0 ⟶ x0 ∈ 0.
Apply EmptyE with
SNoLev x0.
The subproof is completed by applying H2.