Let x0 of type ι be given.
Apply H1 with
False leaving 2 subgoals.
Assume H2: x0 ∈ x0.
Apply In_irref with
x0.
The subproof is completed by applying H2.
Assume H2:
and (x0 = x0) (u2 ∈ u1).
Apply H2 with
False.
Assume H3: x0 = x0.
Apply In_no2cycle with
u1,
u2 leaving 2 subgoals.
The subproof is completed by applying In_1_2.
The subproof is completed by applying H4.