I'm reading Discrete Mathematics and It's application, Rosen, 7-th ed.. By the definition, a simple path of undirected graph contains no repeated edges
But in the proof of following theorem it seems like the definition becomes no repeated vertices
And in the remark following the definition it says: When this terminology is used, the terminology path is often used for a trail with no repeated vertices, $\color{red}{\textrm{conflicting}}$ with the terminology in Definition 1.
But my understanding is
$$\textrm{repeated edges} \implies \textrm{repeated vertices}$$
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There are two possible cases with definition 1, and the subscripts of the resulting path of both are the same as the one in the book, but in one case the path will be cut into two with the statement [...] by deleting the edges correspoding to the vertex sequence $x_i,\dots, x_{j-1}$.
