On the parabolic Hausdorff dimension of orthogonal projections

For Borel sets $A\subset \mathbb{R}^n\times \mathbb{R}$ we prove lower bounds for the parabolic Hausdorff dimension of the orthogonal projections of $A$ on generic $m$-dimensional linear subspaces of $\mathbb{R}^n\times \mathbb{R}$.