Why at 1:55 do we have to prove the inverses of the right coset instead of the inverse of the left coset? Are we making the assumption that H is normal so both left and right cosets are the same?
The original statement of (4) can be proved by assuming (3) is true: Assume (3) is true. Then g_1=g_2h for some h \in H, which is equivalent to g_2=g_1h^{-1} \in g_1H as h^{-1}\in H. So it is not necessary to modify (4) 🤣
