Validity of Run

Many a time we have seen that a batsman while running for run, he losses control over his bat and there is no contact between the batsman and the bat. Still he runs. The completed run is allowed.

Here my question is : whether that run is valid ?

when we refer following laws, and though nowhere in the law it is mentioned that runs should be completed only with the bat in the hand, I think such runs should not be allowed.

Reference:

PAGE NO	LAW NO	DESCRIPTION
11	2.7	The player acting as a runner for a batsman shall carry a bat
20	6.3(a)	Reference to the bat shall imply that the bat is held by the batsman
98	APPENDIX D	Implements of the game: Implement of the game includes bat.
101	--do--	THE BAT : The hand(or hands) holding the bat.
101	--do--	Equipment : a batsman's equipment is his bat
101	--do--	PERSON : A player's person , in case of a batsman, his bat

Referring the above, I think my contention will get some discussion or justice. Wherever referred to batsman/runner, the word bat appears as a must. So while running also, the batsman/runner shall have contact with his bat throughout the act of making and completing the run/runs.