# Reduction from \$HALT\$ to \$A_{TM}\$

I know the reduction to from $$A_{TM}$$ to $$HALT$$. But is the following reduction from $$HALT$$ to $$A_{TM}$$ correct?

We are looking for total computable function $$f$$ mapping from $$HALT$$ to $$A_{TM}$$. The following TM $$F$$ calculates the reduction $$f$$.

``F = on input <T, w>     create the following TM T':     T' = on input v:        start T on v        if T accepts or rejects, *accept*     return <T',w> ``

I think the line `if T accepts or rejects, *accept*` is correct, but it would be great if someone could check this.

Edit: I found the following slides, but I don’t think the construction in there is correct: http://slideplayer.com/slide/13791105/