Select rows based on a minimum in one column

Working with PostgreSQL 9.4, I want a result that takes into consideration only min() (all aggregate functions) values of distance on JOIN or WHERE. But its seems those things are not allowed. So, I am selecting the distance between two points and I want to filter it just to take the min() values into consideration.

To resume the question clearly, suppose these rows:

id; gid; distance; time_interval
142; 028; 62; "21:46:00"
200; 028; 53; "08:20:11"
128; 034; 92; "09:24:43"
179; 034; 70; "08:09:34"
194; 034; 92; "05:31:05"
199; 034; 88; "07:15:48"
200; 034; 61; "14:13:43"
202; 035; 24; "17:32:34"
200; 036; 76; "06:02:11"
154; 037; 97; "12:58:58"
154; 040; 30; "11:34:10"
132; 042; 80; "07:01:12"
142; 042; 67; "19:30:21"

How can I extract id, gid, distance and the time_interval that consider just the min(time_interval) values correspondent to that gid. The problem is that I just can see this with this query:

SELECT id, gid, distance , min(time_interval)
FROM dis
WHERE time_interval = min(time_interval)
GROUP BY id, gid, distance

The result should be:

id; gid; distance; time_interval
200; 028; 53; "08:20:11"
194; 034; 92; "05:31:05"
202; 035; 24; "17:32:34"
200; 036; 76; "06:02:11"
154; 037; 97; "12:58:58"
154; 040; 30; "11:34:10"
132; 042; 80; "07:01:12"

Use DISTINCT ON:

SELECT DISTINCT ON (gid)
       id, gid, distance, time_interval
FROM   dis
ORDER  BY gid, time_interval;  -- more expressions to break ties?

Detailed explanation:

• Select first row in each GROUP BY group?

StackExchange Database Administrators Q#144266, answer score: 13