Let x0 of type ι be given.
Assume H0: x0 ∈ 2.
Apply cases_2 with
x0,
λ x1 . boolToProp x1 ⟶ x1 = 1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply FalseE with
0 = 1.
Apply EmptyE with
0.
The subproof is completed by applying H1.
Let x1 of type ι → ι → ο be given.
Assume H2: x1 1 1.
The subproof is completed by applying H2.