partial_function

Partial function

context	$X,Y$
definiendum	$f\in\text{PartialFunction}(X,Y)$
context	$f \in \text{Rel}(X,Y)$
postulate	$\langle x,a\rangle\in f \land \langle x,b\rangle\in f \Rightarrow a=b$

The definition can be written as

$\{\langle x,a\rangle,\langle x,b\rangle\}\subseteq f \Rightarrow a=b.$

It says that each argument $x$ for the function can result in only one value. (functionality)