reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;
reserve x1,x2,x3,x4,x5,x6,x7,x8,x9,x10 for Element of X;

theorem
  A` = B` implies A = B
proof
  assume A` = B`;
  hence A = B`` .= B;
end;
