Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_6e9d790c24657bc527a0f62de036403ca00386b366ddc02915f8c3a4de529eee with
In x1 (Union x0),
∃ x2 . and (In x1 x2) (In x2 x0),
∃ x2 . and (In x1 x2) (In x2 x0) leaving 3 subgoals.
The subproof is completed by applying unknownprop_0ec9d99c25b180996bbc4b628f77b020efad5688fb0f39be5eb6c4c59a6163b1 with x0, x1.
Assume H2:
∃ x2 . and (In x1 x2) (In x2 x0).
The subproof is completed by applying H2.
Assume H2:
not (∃ x2 . and (In x1 x2) (In x2 x0)).
Apply FalseE with
∃ x2 . and (In x1 x2) (In x2 x0).
Apply notE with
In x1 (Union x0) leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.