Name for theorem : $x \sqsupseteq y \equiv y \sqsubseteq x$

Question

If $\sqsubseteq$ stands for a partial order, I understand that $x \sqsubseteq y$ can be written equivalently as $y \sqsupseteq x$.

I was wondering whether the theorem

$x \sqsupseteq y \equiv y \sqsubseteq x$

has a name?

Answer 1

If you define $y \sqsupseteq x$ to mean $x \sqsubseteq y$, then that is just the definition of $\sqsubseteq$. This is a notational convention used in order theory, not a mathematical result.