after touching women with desire. It is also recommended to perform ablution after cupping, vomiting, and similar occurrences, as reported in the Sunan collections:
“The Prophet—may Allah bless him and grant him peace—vomited and then performed ablution.”
This action indicates only that doing so is recommended. It is not established that he commanded ablution after cupping, nor that he commanded his Companions to perform ablution when wounded, despite the frequency of their wounds. What is reported from the Companions is that they performed ablution, not that they considered it obligatory.
Likewise, laughing aloud during prayer is a sin, and anyone who commits a sin is encouraged to perform ablution. There are two views within the school of Ahmad and other schools concerning whether ablution after laughing aloud is recommended.
As for performing ablution for each prayer in cases of persistent ritual impurity, there are several hadiths from the Prophet—may Allah bless him and grant him peace—some of which have been authenticated by more than one scholar. Thus, the majority’s view that ablution is obligatory for each prayer is better supported. This is the position of Abū Hanīfa, al-Shāfiʿī, and Ahmad. And Allah knows best.
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As for cupping, only those who believe that the fast is broken by what leaves the body, not by what enters it, have considered its being broken by cupping contrary to analogy. Such people have found vomiting, wet dreams, menstrual bleeding, and postnatal bleeding problematic.