  We consider 2d critical Bernoulli percolation on the square lattice. We prove
an approximate color-switching lemma comparing k-arm probabilities for
different polychromatic color sequences. This result is well-known for site
percolation on the triangular lattice in [Nolin08]. To handle the complications
arising from the dual lattice, we introduce a shifting transformation to
convert arms between the primal and dual lattices.
