Let $G$ be a Lie group, let $\pi: P \to M$ be a smooth principal right $G$-bundle, and let $\omega$ be a principal connection on $P$. For $p \in P$, define the holonomy set at $p$ by
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\begin{align*}
\operatorname{Hol}_p(\omega) := \{g \in G : \text{there exists a piecewise smooth loop } \gamma: [0,1] \to M \text{ based at } \pi(p) \text{ such that } \widetilde{\gamma}_p(1) = p g\},
\end{align*}
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where $\widetilde{\gamma}_p: [0,1] \to P$ denotes the $\omega$-horizontal lift of $\gamma$ with $\widetilde{\gamma}_p(0) = p$. Then $\operatorname{Hol}_p(\omega) \le G$.