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Formal proof structure, please A digraph is Eulerian if and only if it is strongly connected...

Formal proof structure, please

A digraph is Eulerian if and only if it is strongly connected and, for every vertex, the indegree equals the outdegree.

You may use the following fact in your proof:

Lemma: Let C be a directed circuit that is a subgraph of some larger directed graph. Then, for any vertex v in V(C), if we count only those arcs in E(C) the out-degree of v is equal to the in-degree of v.

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