Definition:Minimal/Ordered Set/Definition 2

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Let $\left({S, \preceq}\right)$ be an ordered set.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a minimal element of $T$ if and only if:

$\neg \exists y \in T: y \prec x$

where $y \prec x$ denotes that $y \preceq x \land y \ne x$.

That is, if and only if $x$ has no strict predecessor.

Also see