Function restriction-expressible subgroup property

Main definition
A subgroup property $$p$$ is said to be function restriction-expresssible if there exist function properties $$a$$ and $$b$$ such that $$p$$ has a restriction formal expression $$a$$ &rarr; $$b$$ with respect to the function restriction formalism. In other words, a subgroup $$H$$ satisfies $$p$$ in a group $$G$$ if and only if every function in $$G$$ satisfying property $$a$$ restricts to a function on $$H$$ satisfying property $$b$$.

Stronger metaproperties

 * Invariance property: This is a subgroup property that can be expressed using the function restriction formalism with the right side being the property of just being a function.
 * Balanced subgroup property: This is a subgroup property that can be expressed using the function restriction formalism with the left side and the right side being equal.
 * Left-inner subgroup property
 * Left-extensibility-stable subgroup property