What about must be covered by...
Be careful with your tolerances and so forth. Do you really want any "adjacent" line to be snapped to the other line?
And, make a copy of the data before you start. Validating topology changes the geometry permanently.
To add to what Neil mentioned, read the section Marking an error as an exception—Help | ArcGIS for Desktop
Even if you have a rule in place that must be followed by the majority of the lines, there may still be some exceptions. Marking them as such allows you to filter those out when looking for errors.
My experience..When we converted our coverages to a GDB with topology we ended up with many exceptions to the rules I put in place (mainly for the outer polygons that therefore didn't have a shared boundary). But for my peace of mind (and my leaning towards being a control freak) that we where making sure to correct anything that was an error, I felt better about the error popping up and marking it an error rather than not including the rule. But that is me coming from the coverage world that had much more stringent rules that shapes and FC without all the topology rules.
If the topology check for Must Not Have Dangles turned up many issues, you may want to consider running the Snap (Editing) geoprocessing tool:
Chris Donohue, GISP