Belay that.  I misread "proper superset" as "proper superkey".

Sincerely,

Gene Wirchenko

Computerese Irregular Verb Conjugation:
    I have preferences.
    You have biases.
    He/She has prejudices.

"A superkey that does not have the irreducibility property; i.e., a proper
superset of a key."

- The Relational Database Dictionary

I never heard that one either. So, I will make a wild guess :)

Some superkeys are keys with extra columns tacked on the end which can
be tirmmed -- (vin, assigned_parking_space). You might use it to get a
covering index.

Some superkeys have several subsets which are candidate keys -- given
Schedule (teacher, room_nbr, class_period), we could make all three
columns into the key, but (room_nbr, class_period) -> teacher  and
(teacher, class_period) -> room_nbr which gives us other, smaller keys
and no rule for picking which one to use.

Maybe a "proper superkey" is one of these situations?