  It is proven that every flat connection or covariant derivative $\nabla$ on a
left $A$-module $M$ (with respect to the universal differential calculus)
induces a right $A$-module structure on $M$ so that $\nabla$ is a bimodule
connection on $M$ or $M$ is a flat differentiable bimodule. Similarly a flat
hom-connection on a right $A$-module $M$ induces a compatible left $A$-action.
