Corollary 7.4:

If $\gamma_1^\prime,\; \gamma_1^{\prime \prime}$ are homotopic paths starting at $\gamma_0(1)$ then $[\gamma_0 \ast \gamma_1^\prime]= [ \gamma_0 \ast \gamma_1^{\prime \prime}].$ Likewise if $\gamma_1$ is a path in $X$ and $\gamma_0^\prime ,\; \gamma_0^{\prime \prime}$ are homotopic paths whose terminal points are at $\gamma_1(0)$ then $\gamma_0^\prime \ast \gamma_1 \sim \gamma_0^{\prime \prime} \ast \gamma_1.$