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 |^ b |^ A = a |^ (b * A)
proof
  thus a |^ b |^ A = {a} |^ {b} |^ A by Th37
    .= a |^ (b * A) by Th35;
end;
