let A, B be Subset of (TOP-REAL 2); :: thesis: ( A is_inside_component_of B implies UBD B misses A )
assume A is_inside_component_of B ; :: thesis: UBD B misses A
then A c= BDD B by JORDAN2C:22;
hence UBD B misses A by JORDAN2C:24, XBOOLE_1:63; :: thesis: verum