is there hadith about that a cup of milk makes muslim sated?
maybe there is a known false hadith? i do not know how to search for false hadithes.
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First of all while Arabic speakers today mostly refer to milk by الحليب in ahadith it is mostly referred to by the synonym: اللبن this term is also mentioned in the qur'an:
And indeed, for you in grazing livestock is a lesson. We give you drink from what is in their bellies - between excretion and blood - pure milk, palatable to drinkers. (16:66)
Is the description of Paradise, which the righteous are promised, wherein are rivers of water unaltered, rivers of milk the taste of which never changes, rivers of wine delicious to those who drink, and rivers of purified honey, in which they will have from all [kinds of] fruits and forgiveness from their Lord, like [that of] those who abide eternally in the Fire and are given to drink scalding water that will sever their intestines? (47:15)
Secondly often a translation uses terms that are added or changed compared to the original text. For example it is rather uncertain whether the word "cup" was used or only concluded by a translator or implied by a commentary of the hadith.
Further as Arabic language is rich of synonyms and the prophet () had a high level in the linguistics and speech it is not excluded that he used terms that don't directly imply "sated" or "satiation".
What I could find is a hadith on a supplication one should perform when/after eating a meal, that is regarded in most hadith collections as da'if, but al-Albani declared the version from Sunan abi Dawod as "hassan" all this hadith include the following sentence (or similar):
Here the full quote from Sunan abi Daword:
I was in the house of Maymunah. The Messenger of Allah (ﷺ) accompanied by Khalid ibn al-Walid entered. Two roasted long-tailed lizards (dabb) placed on the sticks were brought to him. The Messenger of Allah (ﷺ) spat. Khalid said: I think that you abominate it, Messenger of Allah. He said: Yes. Then the Messenger of Allah (ﷺ) was brought milk, and he drank (it). The Messenger of Allah (ﷺ) then said: When one of you eats food, he should say: O Allah, bless us in it, and give us food (or nourishment) better than it. When he is given milk to drink he should say: O Allah! bless us in it and give us more of it, for no food or drink satisfies like milk.
Abu Dawud said: This is the Musaddad's version.