redundant foreign keys in PostgreSQL - are there any indexing benefits? Note: this is not the same as this SO question which is about adding redundant information in the tables themselves.

Does the final statement in the below series of statements buy me anything in terms of indexing / query optimization or is it totally useless and an anti-pattern? From a referential integrity viewpoint it is useless but might there be some benefit in indexing, or query processing speed for instance, e.g. in a JOIN only between the "child" and "grandfather" tables?

CREATE TABLE grandfather (i INTEGER);
ALTER TABLE  grandfather ADD PRIMARY KEY (i);

CREATE TABLE father  (i, j INTEGER);
ALTER TABLE  father ADD PRIMARY KEY (i, j);
ALTER TABLE  father ADD CONSTRAINT father_2_grandfather FOREIGN KEY (i) REFERENCES grandfather(i);

CREATE TABLE child (i, j, k INTEGER);
ALTER TABLE  child ADD PRIMARY KEY (i, j, k);
ALTER TABLE  child ADD CONSTRAINT child_2_father      FOREIGN KEY (i, j) REFERENCES father(i, j);
-- is the below statement totally useless ?
ALTER TABLE  child ADD CONSTRAINT child_2_grandfather FOREIGN KEY (i)    REFERENCES grandfather(i);
(For similar relations simple hierarchy are more sensible... (id, parent))

Apart from that the last foreign key only slows down a bit the DML queries.