Right tightening

Symbol-free definition
Given a restriction formal expression or extension formal expression for a property, a right tightening of the expression is another formal expression for the same property with the same left side but with the right side stronger than before.

Definition with symbols
Given a restriction formal expression or extension formal expression for a property, say $$a$$ &rarr; $$b$$, a right tightening for the property is another expression $$c$$ &le; $$b$$ such that $$a$$ &rarr; $$c$$ = $$a$$ &rarr; $$b$$.

Maximal right tightening and right tight expressions
For any expression, there is a maximal right tightening, after which no further proper right tightening is possible. A restriction (respectively extension) formal expression for which no further tight tightening is possible is termed a right tight restriction formal expression (respectively right tight extension formal expression). The maximal right tightening operator is thus an idempotent operator on the collection of all restriction formal expressions and its image is the collection of right tight restriction formal expressions.