reserve x,y,y1,y2 for set;
reserve G for Group;
reserve a,b,c,d,g,h for Element of G;
reserve A,B,C,D for Subset of G;
reserve H,H1,H2,H3 for Subgroup of G;
reserve n for Nat;
reserve i for Integer;

theorem
  A * H * a = A * (H * a)
proof
  thus A * H * a = A * (H * {a}) by GROUP_2:97
    .= A * (H * a);
end;
