What exact do the terms mitzamek V’yafa Lo and Mitztamek V’Ra Lo mean in the following cases?
I see the poskim talking about already cooked coffee and how there may not be the prohibtion of cooking it on shabbos even though it is cold liquid because the cooking would be mitzamek V’ra lo. A similar svara is used to explain why reheating dry foods with a little moisture on them is allowed. The liquid being reheated is considered mitztamek v’ra lo.
How is this different than reheating cold soup? In this case I don’t need the item really cooked but just reheated. On the other hand, if the cholent is cooked on friday night, but the cooking over the night makes it better in my mind is that mitzamek vyafu lo.
I am having a hard time drawing the lines between the two concepts.
For purposes of shehiyah, meaning the concern that a person will come to turn up the heat and cook something, if it is “getting better” by being on the fire the situation is considered “mitztamek ve-yafeh lo,” and the concern applies.
The issues of bishul that you mention derive from the ruling of Rabbeinu Yerucham (cited in the Beis Yosef, 253 and 318), who makes a distinction in bishul achar bishul between mitztamek ve-yafeh lo and ra lo.
Although the Rema mentions Rabbeinu Yerucham (318:4), and the Taz rules in accordance, the Bach, the Gra, and the Mishnah Berurah do not go with this, and therefore the standard ruling is that bishul achar bishul is prohibited even when mitztamek ve-ra lo.
For dry foods, there is a sevara of following the “majority of the food,” which is dry, and in this connection Rabbeinu Yerucham mentions the idea of mitztamek ve-yafeh lo (see Peri Megadim). However, the majority of poskim (Shulchan Aruch Harav, and others; see Mishnah Berurah 318:32 and 38) write that the food must be completely dry.
Best wishes, and sorry for the delay in answering.