Let $X$ be a smooth algebraic variety with tangent sheaf $\Theta$ and $M$ a sheaf of modules on $X$. Let $D$ be the sheaf of differential operators on $X$.
Then giving a left $D-$ module structure on $M$ is equivalent to giving a homomorphism
$\nabla: \Theta \rightarrow End(M)$ with
1: $\nabla_{f \theta}(s)=f\nabla_\theta(s)$
2: $\nabla_\theta (fs)=\theta(f)s+f\nabla_\theta(s)$
3: $\nabla_{[\theta_1,\theta_2]}(s)=[\nabla_{\theta_1},\nabla_{\theta_2}](s)$,
where $\theta \in \Theta, f \in O_X, s \in M$.
The module structure is given by $\theta s=\nabla_\theta(s)$ I checked all conditions except associativity, i.e. why can one deduce from 3: that $(\theta_1 \theta_2)s = \theta_1(\theta_2s)$ holds?