Left transiter preserves intersection-closedness

Verbal statement
The left transiter of an intersection-closed subgroup property is again an intersection-closed subgroup property.

Stronger facts

 * Intersection-closedness is left residual-preserved

Related facts

 * Left transiter preserves join-closedness
 * Left transiter preserves upward-closedness
 * Right transiter preserves intermediate subgroup condition
 * Right transiter preserves upper join-closedness