Apply In_ind with
λ x0 . x0 ⊆ V_ x0.
Let x0 of type ι be given.
Assume H0:
∀ x1 . x1 ∈ x0 ⟶ x1 ⊆ V_ x1.
Let x1 of type ι be given.
Assume H1: x1 ∈ x0.
Apply V_I with
x1,
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H0 with
x1.
The subproof is completed by applying H1.