Definition:Strictly Progressing Mapping/Definition 1

Definition
Let $g$ be a mapping. $g$ is a strictly progressing mapping :
 * $\forall x \in \Dom g: x \subsetneqq \map g x$

That is, if $x$ is a proper subset of its image under $g$ for all $x$.

Also see

 * Equivalence of Definitions of Strictly Progressing Mappings