Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H2: x1 ∈ x0.
Apply exactly1of2_E with
x1 ∈ x0,
x1 ∈ minus_SNo x0,
nIn 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.
The subproof is completed by applying H4.
Assume H3:
not (x1 ∈ x0).
Apply FalseE with
x1 ∈ minus_SNo x0 ⟶ nIn x1 (minus_SNo x0).
Apply H3.
The subproof is completed by applying H2.