I'm trying to show  that for every $L \in RE $ , there is    $L\leq_m HALT$.can you tell if my reduction is true?The reduction, while  getting input $x\in L$,builds a T.M machine D, that upon some input   $x_1$, D is running M on $x$,if M halted on x, D accepts and the reduction  returns $<M,x>$. otherwise, D is doing what M does: loop.does it a correct reduction? thanks.
trying to prove that HALT is RE-HARD
computability