reserve G for Group;
reserve A,B for non empty Subset of G;
reserve N,H,H1,H2 for Subgroup of G;
reserve x,a,b for Element of G;

theorem Th17:
  A c= N ~ A
proof
  let x be object;
  assume
A1: x in A;
  then reconsider x9 = x as Element of G;
  x9 in x9 * N  by GROUP_2:108;
  then x9 * N meets A by A1,XBOOLE_0:3;
  hence thesis;
end;
