reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem
  a * H1 * H2 = a * (H1 * H2)
proof
  thus a * H1 * H2 = a * (carr H1 * H2) by GROUP_2:96
    .= a * (H1 * H2);
end;
