Obtaining a property due to being part of a larger whole

Solution 1:

This is an interesting question. After some thought, derive comes into mind.

Derive

to receive or obtain from a source or origin / to trace from a source or origin

Solution 2:

I dont't know if this is what you were looking for, but in some spheres (maths, phylosophy...), this is called the 'transitive property'. In general --and not too technical-- lines, given a, b and c, transitive property establishes that if a is related to b in a specific manner, and b and c are also related, then a and c are related accordingly. Not too long ago, I heard something like this in the TV show called Silicon Valley, from an episode called Adult content. In a scene, EndFrame workers were claimed to be "pieces of sh-t". A certain "he" (I don't remember his name) worked for EndFrame "so, by the transitive property, he is, therefore, also a piece of sh-t." This sounded to me to resemble what you were trying to say. In your case, the transitive property would apply as follows:

• A given sweater (a) is made of woolen (b).
• A given sleeve (c) belongs to that sweater (a).
• Therefore, the sleeve (c) is made of woolen (b) too.

I thought maybe you could work something out from that (what about transitivity or something like that?).