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
  H * a * A = H * (a * A)
proof
  thus H * a * A = H * {a} * A .= H * (a * A) by GROUP_2:98;
end;
