Let x0 of type ι be given.
Assume H0: x0 ∈ 2.
Apply cases_2 with
x0,
λ x1 . not (boolToProp x1) ⟶ x1 = 0 leaving 3 subgoals.
The subproof is completed by applying H0.
Let x1 of type ι → ι → ο be given.
Assume H2: x1 0 0.
The subproof is completed by applying H2.
Apply FalseE with
1 = 0.
Apply H1.
The subproof is completed by applying In_0_1.