Characteristics of Minimally Inductive Class under Progressing Mapping/Image of Proper Subset is Subset

Proof
From Minimally Inductive Class under Progressing Mapping induces Nest, we have that $M$ is a nest in which:
 * $\forall x, y \in M: \map g x \subseteq y \lor y \subseteq x$

Thus corollary $1$ of the Sandwich Principle applies directly.