ThmDex – An index of mathematical definitions, results, and conjectures.
F9690
Formulation 1
Let $f : X \to \mathbb{R}$ be a D4364: Real function.
Let $a, b \in \mathbb{R}$ each be a D993: Real number such that
(i) $a \leq b$
Then \begin{equation} \{ x \in X : f(x) \leq a \} \subseteq \{ x \in X : f(x) \leq b \} \end{equation}