Condition can be pushed from the HAVING clause into the WHERE clause
if it depends only on the fields that are used in the GROUP BY list
or depends on the fields that are equal to grouping fields.
Aggregate functions can't be pushed down.

How the pushdown is performed on the example:

SELECT t1.a,MAX(t1.b)
FROM t1
GROUP BY t1.a
HAVING (t1.a>2) AND (MAX(c)>12);

=>

SELECT t1.a,MAX(t1.b)
FROM t1
WHERE (t1.a>2)
GROUP BY t1.a
HAVING (MAX(c)>12);

The implementation scheme:

1. Extract the most restrictive condition cond from the HAVING clause of
   the select that depends only on the fields that are used in the GROUP BY
   list of the select (directly or indirectly through equalities)
2. Save cond as a condition that can be pushed into the WHERE clause
   of the select
3. Remove cond from the HAVING clause if it is possible

The optimization is implemented in the function
st_select_lex::pushdown_from_having_into_where().

New test file having_cond_pushdown.test is created.