Not ALL of Kashmir is part of the nation calling itself "India". Some of it (78,000 sq.km. is part of the nation calling itself "Pakistan". Then there are the parts currently part of China (5,000 sq.km. contributed by Pakistan and 37,555 contributed by India itself) and Afghanistan (depending on who is drawing the lines).
The situation is actually far more complex than that, and if Tibet ever regains it's independence, Tibet and Kashmir will have overlapping claims to the same desolate mountains.