Restriction to Subset of Strict Total Ordering is Strict Total Ordering
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Let $\prec$ be a strict total ordering on $A$.
Let $T$ be a subset or subclass of $A$.
Then the restriction of $\prec$ to $B$ is a strict total ordering of $B$.
- Restriction of Transitive Relation is Transitive
- Restriction of Antireflexive Relation is Antireflexive
- Restriction of Connected Relation is Connected