Is there Such Thing As The Opposite of Unique Constraint

I want to be constrain my database with what is essentially the opposite of a UNIQUE constraint. I want to only be able to add a new row if some combination of fields has been added before.

Note: I am working within postgres.

Take the following datasets for example. I want a "NON UNIQUE" constraint on the following:

1, a, 1

1, a, 1

1, b, 1

I should not have been able to add the row (1, b, 1) since it has not appeared before. There are also other fields I don't want to constrain so it's not like all the entries are identical.

This may be a separate question, but I would also like to add the constraint that all rows with the same value in one column (i.e. a in the above example) have the same value in another.

So I want this to be impossible

1, a, 1

1, a, 1

0, a, 1

But this is ok

1, a, 1

1, a, 1

0, b, 1

I have looked around pretty heavily and the opposite of this is possible
with unique constraints, but I can't find anything that works for this.
Check constraints will only look at the row in question, and won't take into account the entire table's entries like a unique constraint would.

Is this even possible? Or is this now out of the realms of Postgres functionality, and must be done in-application.

Your second goal can be achieved with an EXCLUDE constraint.

create extension btree_gist ;
alter table t add constraint adsfj exclude using gist (col2 with =, col1 with <>);

StackExchange Database Administrators Q#231296, answer score: 2