Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: x0 ⊆ x1.
Apply set_ext with
binintersect x0 x1,
x0 leaving 2 subgoals.
The subproof is completed by applying binintersect_Subq_1 with x0, x1.
Let x2 of type ι be given.
Assume H1: x2 ∈ x0.
Apply binintersectI with
x0,
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply H0 with
x2.
The subproof is completed by applying H1.