Set of Subgroups forms Complete Lattice/Proof 2

Proof
From Group is Subgroup of Itself:
 * $\struct {G, \circ} \in \mathbb G$

Let $\mathbb H$ be a non-empty subset of $\mathbb G$.

From Intersection of Subgroups is Subgroup: General Result:
 * $\ds \bigcap \mathbb H \in \mathbb G$

Hence, from Set of Subsets which contains Set and Intersection of Subsets is Complete Lattice:


 * $\struct {\mathbb G, \subseteq}$ is a complete lattice

where $\ds \bigcap \mathbb H$ is the infimum of $\mathbb H$.