  We show that for a non-degenerate dimer model, both the first consistency
condition of Mozgovoy and Reineke and the properly-orderedness condition of
Gulotta are equivalent to a condition on zigzag paths, which goes back to
Hanany and Vegh. The last condition is used in arXiv:0905.0059 to study the
behavior of a dimer model under the operation of removing a vertex from the
lattice polygon and taking the convex hull of the rest.
