Order of Subgroup Product/Lemma

Lemma for Order of Subgroup Product
Let $h_1, h_2 \in H$.

Then:
 * $h_1 K = h_2 K$


 * $h_1$ and $h_2$ are in the same left coset of $H \cap K$.
 * $h_1$ and $h_2$ are in the same left coset of $H \cap K$.

Proof
Let $h_1, h_2 \in H$.

Then: