What is $\rightarrowtail$ used for? I have come across this symbol many times, but I am unsure as to how to correctly use it.
So I can read up on it, what is the name of this mapping function?
When would it be correct to use and when wouldn't you use it?
I think it may be used when you haven't specified a function for the mapping, but just a guess.

Example: Any wellordered set $\langle X,\prec\rangle$ is order isomorphic to the set of its segments ordered by $\subset$
Proof: Let $Y=\{X_a\vert a\in X\}$. Then $a\rightarrowtail X_a$ is a (1-1) mapping onto $Y$, and since $a\prec b\Leftrightarrow X_a\subset X_b$ the mapping is order preserving.
Is it necessary to use $\rightarrowtail$ here, could you just use $\mapsto$ or $\rightarrow$, in this example why did we use this symbol?


It is usually used to denote an injection.
