Proposition 13

Let $M_1, M_2$ be two supplementary submodules in an A-module E. The restriction to $M_1$ of the canonical mapping $E \to E/M_2$ is an isomorphism of $M_1$ onto $E/M_2$.

This linear mapping is surjective since $M_1 + M_2 = E$ and it is injective since its kernel is the intersection of $M_1$ and the kernel $M_2$ of $E \to E/M_2$ and hence reduces to $\{0\}$.