Intersection of Finite Set of Submodules is Infimum of Lattice of Submodules

Theorem
Let $R$ be a ring.

Let $\struct {G, +_G}$ be an abelian group.

Let $M = \struct {G, +, \circ}_R$ be an $R$-module.

Let $H_1, H_2, \ldots, H_n$ be submodules of $M$.

Then $H_1 \cap H_2 \cap \cdots \cap H_n$ is the infimum of $\set {H_1, H_2, \ldots, H_n}$ in the complete lattice of all submodules of $M$.