select version();
                                                 version
---------------------------------------------------------------------------------------------------------
 PostgreSQL 11.1 on x86_64-pc-linux-gnu, compiled by gcc (GCC) 4.8.5 20150623 (Red Hat 4.8.5-28), 64-bit
(1 row)


drop table if exists tab1;
DROP TABLE
create table tab1 ( r_object_id char(16) primary key, dcmi_title varchar(250) );
CREATE TABLE
create index tab1__dcmi_title on tab1 ( lower(dcmi_title) );
CREATE INDEX
create or replace function custom_lower(s text) RETURNS text as $$
  SELECT LOWER(s);
$$ LANGUAGE sql;
CREATE FUNCTION
drop table if exists tab2;
DROP TABLE
create table tab2 ( r_object_id char(16) primary key, dcmi_title varchar(250) );
CREATE TABLE
create index tab2__dcmi_title on tab2 ( custom_lower(dcmi_title) );
CREATE INDEX
explain SELECT * FROM ( SELECT r_object_id, lower(dcmi_title) s_dcmi_title from tab1 ) t WHERE s_dcmi_title = 'all aboard 1 poster pack'
;
                                  QUERY PLAN
-------------------------------------------------------------------------------
 Index Scan using tab1__dcmi_title on tab1  (cost=0.14..8.16 rows=1 width=100)
   Index Cond: (lower((dcmi_title)::text) = 'all aboard 1 poster pack'::text)
(2 rows)


explain SELECT * FROM ( SELECT r_object_id, lower(dcmi_title) calculated_col from tab1 WHERE lower(dcmi_title) = 'all aboard 1 poster pack' ) t
;
                                  QUERY PLAN
-------------------------------------------------------------------------------
 Index Scan using tab1__dcmi_title on tab1  (cost=0.14..8.16 rows=1 width=100)
   Index Cond: (lower((dcmi_title)::text) = 'all aboard 1 poster pack'::text)
(2 rows)


explain SELECT * FROM ( SELECT r_object_id, custom_lower(dcmi_title) calculated_col from tab2 WHERE custom_lower(dcmi_title) = 'all aboard 1 poster pack' ) t
;
                                  QUERY PLAN
-------------------------------------------------------------------------------
 Index Scan using tab2__dcmi_title on tab2  (cost=0.14..8.16 rows=1 width=100)
   Index Cond: (lower((dcmi_title)::text) = 'all aboard 1 poster pack'::text)
(2 rows)


explain SELECT * FROM ( SELECT r_object_id, custom_lower(dcmi_title) s_dcmi_title from tab2 ) t WHERE s_dcmi_title = 'all aboard 1 poster pack'
;
                          QUERY PLAN
---------------------------------------------------------------
 Subquery Scan on t  (cost=0.00..13.25 rows=1 width=100)
   Filter: (t.s_dcmi_title = 'all aboard 1 poster pack'::text)
   ->  Seq Scan on tab2  (cost=0.00..11.62 rows=130 width=100)
(3 rows)