we plot the difference in circular velocity at 1 kpc, and at $z=0$, between the DMO and DMB satellites of our semi-analytic calculations. This difference, $\Delta v_{{\rm c,1kpc}}=v_{{\rm c,DMO}}-v_{{\rm c,DMB}}$, is due to the cumulative effects of the two phases of the model: a) the flattening from cuspy to cored of density profiles due to dynamical friction interaction between baryon clumps and DM, and b) tidal stripping and heating from the crossing of the satellite through the host galaxy. The dashed line is a fit to the output points of the model, and is given by $$\begin{aligned}
\Delta(v_{1kpc}) & = & {\rm 0.3v_{infall}-0.3km/s}\nonumber \\
 &  & {\rm 10km/s<v_{infall}<50km/s}\label{eq:mia}\end{aligned}$$

This correction is then applied to VL2 and is close to the results found by Z12 in the form $$\begin{aligned}
\Delta(v_{1kpc}) & = & {\rm 0.2v_{infall}-0.26km/s}\nonumber \\
 &  & {\rm 20km/s<v_{infall}<50km/s.}\end{aligned}$$

They obtained the above equation by fitting the output of their model, based on SF and tidal stripping, as displayed on their Fig. 8. Our Fig. \[fig:DMO-DMB\] shows a clearer trend $\Delta v_{c}$-$v_{{\rm infall}}$, as it doesn’t suffer from the numerical effect, described in Z12 (see their Sect. 4 of B13), of inefficient stripping in SPH simulations.In addition, Z12 neglects disk 