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 Th60:
  H |^ a |^ b = H |^ (a * b)
proof
  the carrier of H |^ a |^ b = carr(H |^ a) |^ b by Def6
    .= (carr H |^ a) |^ b by Def6
    .= carr H |^ (a * b) by Th47
    .= the carrier of H |^ (a * b) by Def6;
  hence thesis by GROUP_2:59;
end;
