What is the ruling on someone who, while performing one prayer, thought they were performing another, and thus sat for the Tashahhud before completing the required number of rak'ahs, or stood up before completing them?

If someone intended a prayer and then, during it, thought they were in another prayer, but then remembered, their prayer is valid. If this thought led to an action that necessitates prostration of forgetfulness (sujud al-sahw), such as an extra sitting, then prostration of forgetfulness becomes obligatory. However, if no action necessitating prostration occurred, then the prayer is valid and nothing is required.