Definition:Rooted Tree/Ancestor Node

Definition
Let $T$ be a rooted tree with root $r_T$.

Let $t$ be a node of $T$.

An ancestor node of $t$ is a node in the path from $t$ to $r_T$.

This path is indeed unique, by Path in Tree is Unique.

Proper Ancestor
A proper ancestor node of $t$ is an ancestor node of $t$ that is not $t$ itself.