reserve X for set,
        D for a_partition of X,
        TG for non empty TopologicalGroup;
reserve A for Subset of X;

theorem
  for V being a_neighborhood of 1_TG holds
    V" is a_neighborhood of 1_TG
  proof
    let V be a_neighborhood of 1_TG;
    V" is a_neighborhood of (1_TG)" by TOPGRP_1:54;
    hence thesis by GROUP_1:8;
  end;
