Let x0 of type ι be given.
Let x1 of type ι be given.
Apply PNoLe_antisym with
SNoLev x0,
SNoLev x1,
λ x2 . x2 ∈ x0,
λ x2 . x2 ∈ x1,
x0 = x1 leaving 5 subgoals.
Apply SNoLev_ordinal with
x0.
The subproof is completed by applying H0.
Apply SNoLev_ordinal with
x1.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Assume H5:
PNoEq_ (SNoLev x0) (λ x2 . x2 ∈ x0) (λ x2 . x2 ∈ x1).
Apply SNo_eq with
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
The subproof is completed by applying H5.