Referential integrity based on data more than a table away

Notes on tables A, B, C, D, E

• B.aid and C.aid reference A.aid.
• D.cid references C.cid and D.did is the primary key. D is a C.
• cid and did are pre-assigned and I cannot change them (they need to remain separate despite the is-a).
• E has information that depends on its primary key (bid, did) with bid referencing B.bid and did referencing D.did.

Is there a way to make sure that the bid and did of a given row in E reference rows in B and D that reference the same row in A (through C in the case of D)?

So far I've come up with

CREATE TABLE a (    aid INTEGER PRIMARY KEY);CREATE TABLE b (    bid INTEGER PRIMARY KEY,    aid INTEGER NOT NULL REFERENCES a ( aid ),    UNIQUE ( bid, aid ));CREATE TABLE c (    cid INTEGER PRIMARY KEY,    aid INTEGER NOT NULL REFERENCES a ( aid ),    UNIQUE ( cid, aid ));CREATE TABLE d (    did INTEGER PRIMARY KEY,    cid INTEGER NOT NULL REFERENCES c ( cid ),    UNIQUE ( did, cid ));CREATE TABLE e (    bid INTEGER NOT NULL REFERENCES b ( bid ),    cid INTEGER NOT NULL REFERENCES c ( cid ),    did INTEGER NOT NULL REFERENCES d ( did ),    dcid INTEGER NOT NULL,    baid INTEGER NOT NULL,    caid INTEGER NOT NULL,    PRIMARY KEY ( bid, did ),    FOREIGN KEY ( bid, baid ) REFERENCES b ( bid, aid ),    FOREIGN KEY ( cid, caid ) REFERENCES c ( cid, aid ),    FOREIGN KEY ( did, dcid ) REFERENCES d ( did, cid ),    CHECK ( baid = caid AND cid = dcid ));

Is there a better way to create E that doesn't seem so complicated and redundant?