Let x0 of type ι be given.
Apply set_ext with
binintersect x0 x0,
x0 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with x0, x0.
Apply binintersect_Subq_max with
x0,
x0,
x0 leaving 2 subgoals.
The subproof is completed by applying Subq_ref with x0.
The subproof is completed by applying Subq_ref with x0.