\gamma_{1} \equiv \gamma_{2} \Leftrightarrow \left\{ \begin{array}{l}
\gamma_{1}(0) = \gamma_{2}(0) = p,\text{\ and\ } \\
\left. \frac{\mathrm{d}}{\mathrm{d}t}\phi \circ \gamma_{1}(t) \right|_{t = 0} = \left. \frac{\mathrm{d}}{\mathrm{d}t}\phi \circ \gamma_{2}(t) \right|_{t = 0} \\
\end{array} \right.
