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_CSNo x1 ∈ SNoS_ x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply minus_SNo_minus_CSNo with
x1,
λ x2 x3 . x2 ∈ SNoS_ x0 leaving 2 subgoals.
The subproof is completed by applying H4.
Apply minus_SNo_SNoS_ with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.