Let x0 of type ι be given.
Apply SNo_eq with
x0,
0 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Apply SNoLev_0 with
λ x1 x2 . SNoLev x0 = x2.
The subproof is completed by applying H1.
Apply H1 with
λ x1 x2 . SNoEq_ x2 x0 0.
Let x1 of type ι be given.
Assume H2: x1 ∈ 0.
Apply FalseE with
iff (x1 ∈ x0) (x1 ∈ 0).
Apply EmptyE with
x1.
The subproof is completed by applying H2.