Power Function Preserves Ordering in Ordered Group/Corollary

Corollary to Power Function Preserves Ordering in Ordered Group
Let $\struct {G, \circ, \preccurlyeq}$ be an ordered group with identity $e$.

Let $\prec$ be the reflexive reduction of $\preceq$.

Let $x \in G$.

Let $n \in \N_{>0}$ be a strictly positive integer.

Then the following hold: