Coset Space forms Partition

Theorem
Let $G$ be a group, and let $H \le G$. The left coset space of $H$ forms a partition of its group $G$, and hence:

Similarly, the right coset space of $H$ forms a partition of its group $G$:

Proof
Follows directly from:


 * Congruence Modulo Subgroup is Equivalence Relation
 * Relation Partitions Set iff Equivalence.