Relaxing constraints on BitmapAnd eligibility?

Hi!

I've been investigating why postgres does not do BitmapAnd of two
well-suited indexes, and reading indxpath.c

In my case, there is a table (d date, col1 int, col2 int) -- types not
really important -- and there are two indices on (d,col1) and (d, col2).

For queries that do WHERE d>=X AND col1=Y AND col2=Z postgres will never
BitmapAnd those two indices because both indexes include (d) and we have a
condition on (d). Here is a full example, which could also be seen here:
https://www.db-fiddle.com/f/uPLx5bRtDEoZw3Dx4kkwKh/0:

begin;

CREATE TABLE test_table (
d date,
col1 int,
col2 int
);

INSERT INTO test_table (d, col1, col2)
SELECT
d.date,
c1.val as col1,
c2.val as col2
FROM
generate_series(
'2023-01-01'::date,
'2023-12-31'::date,
'1 day'::interval
) as d(date),
generate_series(1, 1000) as c1(val),
generate_series(1, 1000) as c2(val)
WHERE
random() < 0.001;

create index on test_table(col1,d);
create index on test_table(col2,d);

-- This uses BitmapAnd
explain select * from test_table where col1=123 and col2=321;

-- This does not use BitmapAnd, even though it could!
explain select * from test_table where col1=123 and col2=321 and d >=
'2023-05-05';

I checked that BitmapAnd is rejected by this
<https://github.com/postgres/postgres/blob/master/src/backend/optimizer/path/indxpath.c#L1878>
line in choose_bitmap_and:

if (bms_overlap(pathinfo->clauseids, clauseidsofar))
continue; /* consider it redundant */

There is a comment on choose_bitmap_and that explains the rationale of this
check, but reading it I can't help but feel that what the comment
describes is this condition:

if (bms_is_subset(pathinfo->clauseids, clauseidsofar))
continue; /* consider it redundant */

And indeed, in my (admittedly not super-extensive) testing changing
bms_overlap to bms_is_subset leads to better faster execution plans.

Is it possible that this condition could thus be relaxed?

Even if I am wrong, and the condition absolutely should be bms_overlap, I
feel that this restriction is very very hard to discover and perhaps
https://www.postgresql.org/docs/current/indexes-bitmap-scans.html should
mention that compound indexes that have columns in common will never be
combined?

Best regards, Dmytro