Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x0 . nIn x0 x0.
Let x0 of type ι be given.
Assume H0:
∀ x1 . In x1 x0 ⟶ nIn x1 x1.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with
x0,
x0.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x0,
x0 leaving 2 subgoals.
Apply H0 with
x0.
The subproof is completed by applying H1.
The subproof is completed by applying H1.