Is ghusl required upon waking up and finding a small amount of semen without having had a wet dream?

If you ascertain that semen has been discharged from you during sleep, even if only a small amount, then ghusl (definition) (ritual bath) is obligatory upon you. It is not a condition to remember the wet dream, due to what Aisha, may Allah be pleased with her, narrated: that the Prophet, peace and blessings be upon him, was asked about a man who finds wetness but does not remember a wet dream, he said: "He should perform ghusl." And about a man who sees that he had a wet dream but does not see any wetness, he said: "Ghusl is not required of him."