Right tightness theorem

For function restriction expressions for subgroup properties
Suppose $$a$$ and $$b$$ are properties of functions from a group to itself, and $$p$$ is a subgroup property with the function restriction expression:

$$a \to b$$.

In other words, a subgroup $$H$$ satisfies property $$p$$ in a group $$G$$ if and only if every function from $$G$$ to itself satisfying property $$a$$ in $$G$$, restricts to a function from $$H$$ to itself satisfying property $$b$$ in $$H$$.

Then:
 * If $$a \to b$$ is a right tight function restriction expression, i.e., if $$b$$ cannot be strengthened further without changing $$a$$, then the left transiter for $$p$$ is the subgroup property $$b \to b$$.
 * Otherwise, compute the property $$c$$ such that $$a \to c$$ is a right tightening for $$a \to b$$. Then the left transiter of $$p$$ is the property $$c \to c$$.