Apply In_ind with
λ x0 . TransSet (V_ x0).
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H2: x2 ∈ x1.
Apply V_E with
x1,
x0,
x2 ∈ V_ x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ι be given.
Assume H3: x3 ∈ x0.
Apply V_In_or_Subq with
x0,
x3,
V_ x3 ⊆ V_ x0 leaving 2 subgoals.
Apply FalseE with
V_ x3 ⊆ V_ x0.
Apply unknownprop_5010201a6e1d38348477b9de5ff66e9d31670bdeefdbe08b8723a3d6e30b48d2 with
x3.
Apply H0 with
x3,
x0,
x3 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H5.
The subproof is completed by applying H3.
Assume H5:
V_ x3 ⊆ V_ x0.
The subproof is completed by applying H5.
Apply L5 with
x2.
Apply H4 with
x2.
The subproof is completed by applying H2.