Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H1:
x1 ∈ SNoS_ x0.
Apply SNoS_E2 with
x0,
x1,
minus_SNo x1 ∈ SNoS_ x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply minus_SNo_SNo_ with
SNoLev x1,
x1 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
Apply SNoS_I with
x0,
minus_SNo x1,
SNoLev x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying L6.