Checking if result of st_difference is empty

I am trying to select lines that completely touch a polygon (not at just a single point).

I would assume it would be a simple case of st_isempty(st_difference(geom_a,geom_b)).

However, this is not the case as you can see in the following picture.

I would like to only have the highlight yellow lines returned. What am I doing wrong?

(I could solve it with a string comparison, but I would like to avoid the extra "st_astext" invocation).

The query:

SELECT a.geometry, 
       a.id as a_id, 
       b.FID as b_id,
       st_astext(ST_GeometryN(st_difference(a.geometry,b.geometry),1)) as st_difference,
       st_isempty(ST_GeometryN(st_difference(a.geometry,b.geometry),1)) as st_isempty
FROM a
INNER JOIN b ON st_touches(a.geometry,b.geometry)

SELECT a.geometry, 
       a.id as a_id, 
       b.FID as b_id,
       st_astext(ST_GeometryN(st_difference(a.geometry, b.geometry), 1)) as st_difference,
       ST_IsValid(ST_GeometryN(st_difference(a.geometry, b.geometry), 1)) as st_isvalid
FROM a 
INNER JOIN b ON st_touches(a.geometry, b.geometry)