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A simple local proof of Noether's Second Theorem is given. This proofimmediately leads to a generalization of the theorem, yielding conservationlaws and/or explicit relationships between the Euler--Lagrange equations of anyvariational problem whose symmetries depend upon a set of free orpartly-constrained functions. Our approach extends further to deal with finitedifference systems. The results are easy to apply; several well-knowncontinuous and discrete systems are used as illustrations.

Extensions of Noether's Second Theorem: from continuous to discrete systems