As @ErnieS0 states, there should not be any double taxed income. DC has a tax reciprocity agreement with VA (with every state as matter of fact). That means all income earned while working in DC but living in another state is taxed by your resident state only.
You would "delete" the credit for taxes paid to another state. Your part-year VA return should have the VA income from box 16 in the VA line on your W2. That income would be VA residence income.
Your DC return would have the amount from box 16 in the DC line to cover your DC residence period.
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