Definition:Tree (Set Theory)/Subtree
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Definition
Let $\struct {T, \preceq}$ be a tree.
A subtree of $\struct {T, \preceq}$ is an ordered subset $\struct {S, \preceq}$ with the property that:
- for every $\forall s \in S: \forall t \in T: t \preceq s \implies t \in S$
That is, such that $\struct {S, \preceq}$ is a lower closure of $\struct {T, \preceq}$.