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 Th52:
  A |^ 1_G = A
proof
  thus A |^ 1_G = (1_G)" * A * 1_G by Th50
    .= (1_G)" * A by GROUP_2:37
    .= 1_G * A by GROUP_1:8
    .= A by GROUP_2:37;
end;
