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You must execute the code again to save those values in the database.

PRAGMA foreign_keys = ON;

CREATE TABLE first(
  first_id INTEGER,
  PRIMARY KEY(first_id)
);

CREATE TABLE second(
  first_id INTEGER,
  second_id INTEGER,
  PRIMARY KEY(first_id, second_id),
  FOREIGN KEY (first_id) REFERENCES first(first_id) ON DELETE CASCADE ON UPDATE CASCADE
);

CREATE TABLE third(
  first_id INTEGER,
  third_id INTEGER,
  PRIMARY KEY(first_id, third_id),
  FOREIGN KEY (first_id) REFERENCES first(first_id) ON DELETE CASCADE ON UPDATE CASCADE
);

CREATE TABLE fourth(
  first_id INTEGER,
  second_id INTEGER,
  third_id INTEGER,
  some_property INTEGER,
  PRIMARY KEY(first_id, second_id, third_id, some_property),
  FOREIGN KEY(first_id, second_id) REFERENCES second(first_id, second_id) ON DELETE CASCADE ON UPDATE CASCADE,
  FOREIGN KEY(first_id, third_id) REFERENCES third(first_id, third_id) ON DELETE CASCADE ON UPDATE CASCADE
);

INSERT INTO first(first_id) VALUES (1);
INSERT INTO second(first_id, second_id) VALUES(1,1);
INSERT INTO third(first_id, third_id) VALUES(1,1);
INSERT INTO fourth(first_id, second_id, third_id, some_property) VALUES(1,1,1,1);

UPDATE first SET first_id=first_id - 1;

SELECT * FROM first;
SELECT * FROM second;
SELECT * FROM third;
SELECT * FROM fourth;

first_id
0

first_id	second_id
0	1

first_id	third_id
0	1

first_id	second_id	third_id	some_property
0	1	1	1