Exercise 4, § 1

Let G, G' be two locally compact groups, V (resp. V') an open neighborhood of the neutral element of G (resp. G'), $\varphi$ a local isomorphism of G' with G, defined on V', such that $\varphi(V') = V$. Show that $\Delta_G \circ \varphi$ is the restriction of $\Delta_{G'}$ to V'.