Apply In_ind with
λ x0 . ∀ x1 x2 . x0 ∈ x1 ⟶ x1 ∈ x2 ⟶ x2 ∈ x0 ⟶ False.
Let x0 of type ι be given.
Assume H0:
∀ x1 . x1 ∈ x0 ⟶ ∀ x2 x3 . x1 ∈ x2 ⟶ x2 ∈ x3 ⟶ x3 ∈ x1 ⟶ False.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H1: x0 ∈ x1.
Assume H2: x1 ∈ x2.
Assume H3: x2 ∈ x0.
Apply H0 with
x2,
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H3.
The subproof is completed by applying H1.
The subproof is completed by applying H2.