Information_schema.triggers doesn't show schema for system triggers

CREATE TABLE t (a int);

CREATE TRIGGER tr1 BEFORE INSERT ON t FOR EACH ROW SET @x=1;

CREATE TRIGGER tr2 AFTER STARTUP SET @y=1;

SELECT TRIGGER_NAME, TRIGGER_SCHEMA, EVENT_OBJECT_SCHEMA, EVENT_MANIPULATION

FROM information_schema.TRIGGERS 

WHERE TRIGGER_NAME IN ('tr1','tr2') 

ORDER BY TRIGGER_NAME;

SELECT db,name FROM mysql.event WHERE name='tr2';

DROP TRIGGER tr1;

DROP TRIGGER tr2;

DROP TABLE t;

TRIGGER_NAME	TRIGGER_SCHEMA	EVENT_OBJECT_SCHEMA	EVENT_MANIPULATION

tr1	test	test	INSERT

tr2			STARTUP

SELECT db,name FROM mysql.event WHERE name='tr2';

db	name

test	tr2