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) (u5 ∈ u3).
Apply H2 with
False.
Assume H3: x0 = x0.
Apply In_no2cycle with
u3,
u5 leaving 2 subgoals.
The subproof is completed by applying In_3_5.
The subproof is completed by applying H4.