Apply In_ind with
λ x0 . ∀ x1 x2 x3 . x0 ∈ x1 ⟶ x1 ∈ x2 ⟶ x2 ∈ x3 ⟶ x3 ∈ x0 ⟶ False.
Let x0 of type ι be given.
Assume H0:
∀ x1 . x1 ∈ x0 ⟶ ∀ x2 x3 x4 . x1 ∈ x2 ⟶ x2 ∈ x3 ⟶ x3 ∈ x4 ⟶ x4 ∈ x1 ⟶ False.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H1: x0 ∈ x1.
Assume H2: x1 ∈ x2.
Assume H3: x2 ∈ x3.
Assume H4: x3 ∈ x0.
Apply H0 with
x3,
x0,
x1,
x2 leaving 5 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.