File: differentiable_manifold.tex

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   \gamma_1\equiv \gamma_2 \iff \left\{ \begin{array}{l} \gamma_1(0)=\gamma_2(0)=p, \text{ and }\\ [1.0ex]
   \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.