Is repetition of the prayer necessary after performing Tayammum for an impurity on the body when washing was impossible?

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There are two reported views regarding whether repetition (I'adah) of the prayer is necessary after performing Tayammum for an impurity and praying. Abu Al-Khattab stated that if the impurity is on a wound such that its removal causes harm, Tayammum and prayer are performed without requiring repetition. However, if Tayammum is performed for an impurity while water is unavailable, repetition is required according to him. The companions (As'habuna) of the primary opinion maintain that repetition is not obligatory, based on the Prophet's saying: "The earth (dust/soil) is sufficient for you until you find water." They also reason that since Tayammum substitutes for the purification of ritual impurity, repetition is not required, similar to when Tayammum is performed for an impurity on a wound that is harmful to remove. Moreover, if one prayed without performing Tayammum in that situation, repetition would not be required, making it even less required with Tayammum.