Relation Total-On

Arity: 2
A relation R is TOTAL-ON a domain class C if there are tuples in the relation (x,y) for every instance x of C. If the domain is a relation D, it represents a Cartesian product, and the relation is total on D if for every tuple (x1, x2, ... xn) in D there is a tuple (x1, x2, ... xn, y) in R.
Instance-Of: Binary-Relation, Relation, Set

Equivalence Axioms for Total-On:

(<=> (Total-On ?Relation ?Domain-Relation)
     (Subrelation-Of (Exact-Domain ?Relation) ?Domain-Relation))