{
1: [{start:0, finish: 12}],
2: [{start:0, finish: 12}, {start:12, finish:17}],
3: [{start:12, finish: 17}],
4: [{start:0, finish: 12}],
5: [{start:12, finish:17}, {start:17, finish: 0}],
6: [{start:0, finish: 12}, {start:12, finish:17}],
7: [{start:17, finish: 0}]
}

SELECT * FROM users WHERE
timetable <@ {1: [{start: 0, finish: 12}]} OR timetable <@ {1: [{start: 12, finish: 17}]} OR timetable <@ {1: [{start: 17, finish: 0}]} OR
timetable <@ {2: [{start: 0, finish: 12}]} OR timetable <@ {2: [{start: 12, finish: 17}]} OR timetable <@ {2: [{start: 17, finish: 0}]} OR
......
timetable <@ {7: [{start: 0, finish: 12}]} OR timetable <@ {7: [{start: 12, finish: 17}]} OR timetable <@ {7: [{start: 17, finish: 0}]}

CREATE OR REPLACE FUNCTION weekly_activity(timetable jsonb) RETURNS integer AS $$
    BEGIN
         IF timetable <@ {1: [{start: 0, finish: 12}]} OR timetable <@ {1: [{start: 12, finish: 17}]} THEN
           RETURN 111;
         END IF;
    END;
    $$ LANGUAGE plpgsql IMMUTABLE;

    CREATE INDEX CONCURRENTLY idx_weekly_activity ON table BTREE( weekly_activity(timetable))

    SELECT * FROM table WHERE weekly_activity(timetable) = 111;

CREATE TYPE dow AS ENUM (
  'Monday', 'Tuesday', 'Wednesday', 'Thursday',
  'Friday', 'Saturday', 'Sunday'
);

CREATE FUNCTION time_subtype_diff(x time, y time)
RETURNS float8 AS $$
  SELECT EXTRACT(EPOCH FROM (x - y))
$$ LANGUAGE sql
STRICT IMMUTABLE;

CREATE TYPE timerange AS RANGE (
    subtype = time,
    subtype_diff = time_subtype_diff
);

CREATE TABLE available (
  user_id  int,  -- REFERENCES users,
  dow      dow,
  trange  timerange,
  PRIMARY KEY (user_id, dow)
);

CREATE TABLE users(user_id) AS VALUES (1::int);

INSERT INTO available VALUES
  ( 1, 'Monday', '[13:42,16:12]' );

SELECT *
FROM users AS u
JOIN available AS a USING (user_id)
WHERE dow = 'Monday' AND a.trange @> '[14:00,15:00]';