Strict Lower Closure of G-Tower is Set of Elements which are Proper Subsets

Theorem
Let $M$ be a class.

Let $g: M \to M$ be a progressing mapping on $M$.

Let $M$ be a $g$-tower.

Let $x \in M$.

Then the strict lower closure of $x$ is the set of all elements of $M$ that are proper subsets of $M$.

Proof
Follows directly from the definitions.