Definition:Strictly Well-Founded Relation

Definition
Let $\left({S, \prec}\right)$ be a relational structure.

Then $\prec$ is a Foundational Relation on $A$ iff every nonempty subset of $A$ has a least element.

That is, expressed symbolically:


 * $( \prec Fr A \iff \forall x: \left({x \subseteq A \land x \ne \varnothing}\right) \implies \exists y \in x: \forall z \in x: \left({y = z \lor y \prec z}\right) )$

where $\varnothing$ is the empty set.