Suppose UUU is a subspace of VVV adn v1+U,…,vm+Uv_1+U,\dots,v_m+Uv1+U,…,vm+U is a basis of V/UV/UV/U and u1,…,unu_1,\dots,u_nu1,…,un is a basis of UUU. Prove that v1,…,vm,u1,…,unv_1,\dots,v_m,u_1,\dots,u_nv1,…,vm,u1,…,un is a basis of VVV.
TODO