Balanced subgroup property (generic notion)

''This article is about the general notion of balanced subgroup property. For the typical use of balanced subgroup property in the context of the function restriction formalism, refer balanced subgroup property (function restriction formalism)''.

Symbol-free definition
We need to have two inputs with respect to which we can talk of balanced subgroup property:


 * A relational mapping system
 * A specification of one of these formalisms based on the relational mapping system: the restriction formalism, the extension formalism, the [universal restriction formalism, the universal extension formalism, the when-defined restriction formalism, the when-defined extension formalism

For a given formalism based on the relational mapping system, a subgroup property is termed balanced if it has a formal expression (in that formalism) with equal left and right sides.

Definition with symbols
We need to have two inputs with respect to which we can talk of balanced subgroup property:


 * A relational mapping system
 * A specification of one of these formalisms based on the relational mapping system: the restriction formalism, the extension formalism, the [universal restriction formalism, the universal extension formalism, the when-defined restriction formalism, the when-defined extension formalism

For a given formalism based on the relational mapping system, a subgroup property is termed balanced if it has a formal expression (in that formalism) of the form $$a$$ &rarr; $$a$$.