Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply set_ext with
binintersect x0 (binintersect x1 x2),
binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply binintersect_Subq_max with
binintersect x0 x1,
x2,
binintersect x0 (binintersect x1 x2) leaving 2 subgoals.
Apply binintersect_Subq_max with
x0,
x1,
binintersect x0 (binintersect x1 x2) leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with
x0,
binintersect x1 x2.
Apply Subq_tra with
binintersect x0 (binintersect x1 x2),
binintersect x1 x2,
x1 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_2 with
x0,
binintersect x1 x2.
The subproof is completed by applying binintersect_Subq_1 with x1, x2.
Apply Subq_tra with
binintersect x0 (binintersect x1 x2),
binintersect x1 x2,
x2 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_2 with
x0,
binintersect x1 x2.
The subproof is completed by applying binintersect_Subq_2 with x1, x2.
Apply binintersect_Subq_max with
x0,
binintersect x1 x2,
binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply Subq_tra with
binintersect (binintersect x0 x1) x2,
binintersect x0 x1,
x0 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with
binintersect x0 x1,
x2.
The subproof is completed by applying binintersect_Subq_1 with x0, x1.
Apply binintersect_Subq_max with
x1,
x2,
binintersect (binintersect x0 x1) x2 leaving 2 subgoals.
Apply Subq_tra with
binintersect (binintersect x0 x1) x2,
binintersect x0 x1,
x1 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with
binintersect x0 x1,
x2.
The subproof is completed by applying binintersect_Subq_2 with x0, x1.
The subproof is completed by applying binintersect_Subq_2 with
binintersect x0 x1,
x2.