Chris Brown's Attorney -- Here's Proof the D.A.'s Lying About Community Service

Chris Brown's attorney is firing back at the District Attorney's allegation Chris, and others, lied about the completion of his 180 hours of community service ... and he's filed legal docs to prove it.

Mark Geragos filed his response to the D.A.'s scathing motion ... and claims prosecutors omitted some key facts.

In his docs, Geragos refutes the D.A.'s claim that "no human being ever witnessed" Chris performing community labor -- claiming Richmond's deputy police chief "observed Brown working very hard at cleaning the brush at the [police] stables."

Geragos' filing also includes invoices and checks indicating Chris paid $31,534.70 to the Richmond PD for providing security during his labor details -- which the D.A. claimed Chris didn't pay ... according to Geragos.

According to the documents ... Richmond PD's general counsel also sent the D.A. documents showing Chris did some of his required community service -- back in 2009 and 2010 -- at various police precincts.

Nowhere in the filing does Geragos refer to the Tappahannock Children's Center ... where Chris says he frequently performed odd jobs. The D.A. has questioned the bookkeeping of Chris' hours there because Chris' mom filled out his paperwork, and was once the director of the center.