Let x0 of type ι be given.
Let x1 of type ι be given.
Apply exactly1of2_E with
x1 ∈ x0,
x1 ∈ minus_SNo x0,
x1 ∈ minus_SNo x0 leaving 3 subgoals.
Apply minus_SNo_exactly1of2 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Assume H3: x1 ∈ x0.
Apply FalseE with
not (x1 ∈ minus_SNo x0) ⟶ x1 ∈ minus_SNo x0.
Apply H2.
The subproof is completed by applying H3.
Assume H3:
not (x1 ∈ x0).
The subproof is completed by applying H4.