Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with
∃ x2 . and (In x2 x0) (not (∃ x3 . and (In x3 x0) (In x3 x2))).
Claim L2:
∀ x2 . nIn x2 x0Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with
λ x2 . nIn x2 x0.
Let x2 of type ι be given.
Assume H2:
∀ x3 . In x3 x2 ⟶ nIn x3 x0.
Apply unknownprop_b30a94f49240f0717f4ecb200a605aa8a4e6dad6dc5d1afa60c37866ee96baab with
x2,
x0.
Apply notE with
∃ x3 . and (In x3 x0) (not (∃ x4 . and (In x4 x0) (In x4 x3))) leaving 2 subgoals.
The subproof is completed by applying H1.
Let x3 of type ο be given.
Assume H4:
∀ x4 . and (In x4 x0) (not (∃ x5 . and (In x5 x0) (In x5 x4))) ⟶ x3.
Apply H4 with
x2.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
In x2 x0,
not (∃ x4 . and (In x4 x0) (In x4 x2)) leaving 2 subgoals.
The subproof is completed by applying H3.
Apply unknownprop_e284d5f5a7c3a1c03631041619c4ddee06de72330506f5f6d9d6b18df929e48c with
∃ x4 . and (In x4 x0) (In x4 x2).
Assume H5:
∃ x4 . and (In x4 x0) (In x4 x2).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x4 . In x4 x0,
λ x4 . In x4 x2,
False leaving 2 subgoals.
The subproof is completed by applying H5.
Let x4 of type ι be given.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x4,
x0 leaving 2 subgoals.
Apply H2 with
x4.
The subproof is completed by applying H7.
The subproof is completed by applying H6.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying L2 with x1.
The subproof is completed by applying H0.