Uniform RSW crossing estimate (${\inf }_n{h}_p(n,n)\ge \delta ⟹{\inf }_n{h}_p(\lceil \rho n\rceil ,n)\ge c(\delta ,\rho )$)

For independent bond percolation on the square lattice, a positive uniform lower bound for square crossings implies a positive uniform lower bound for rectangle crossings of every fixed aspect ratio $\rho >1$. The RSW reflection extension lemma first extends a square to aspect ratio $3/2$. Overlapping rectangles and transverse overlap-square crossings then glue using the Harris-FKG inequality. The required constant depends on $\delta$ and $\rho$, not on scale. At a self-dual parameter, dual crossings also give a uniform upper bound below one.