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 Th47:
  A |^ a |^ b = A |^ (a * b)
proof
  thus A |^ a |^ b = A |^ (a * {b}) by Th35
    .= A |^ (a * b) by GROUP_2:18;
end;
