Is ghusl obligatory upon the discharge of something after imagining sexual intercourse, or is its obligation confined to the penetration of the two circumcised parts?

The meeting of the two circumcised parts or the emission of semen with desire necessitates ghusl, even if no semen is emitted, or if it occurs after ghusl following intercourse. This is based on the hadith "Water is from water" and the hadith of Umm Sulaym, "Yes, if she sees water." However, if what is discharged is madhy (pre-seminal fluid), ghusl is not required; rather, only wudu' and washing what has soiled the garment or body are necessary.