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?
Name for theorem : $x \sqsupseteq y \equiv y \sqsubseteq x$
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order-theory
1 Answers
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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.