  For difference variational problems on lattice, this paper presents a
relation between divergence variational symmetries and conservation laws for
the associated Euler-Lagrange system provided by Noether's theorem. This hence
inspires us to define conservation laws related with symmetries for arbitrary
difference equations with or without Lagrangian formulations. These
conservation laws are constrained by some partial differential equations
obtained from the symmetries generators. It is shown that the orders of these
partial differential equations have been reduced comparing to the ones used in
a general approach. Illustrating examples are presented.
