reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: SETWISEO:1
  {A} c= {B} implies A = B
proof
  assume
A1: {A} c= {B};
  now
    let i be object;
    assume
A2: i in I;
    then {A}.i c= {B}.i by A1;
    then {A}.i c= {B.i} by A2,Def1;
    then {A.i} c= {B.i} by A2,Def1;
    hence A.i = B.i by ZFMISC_1:18;
  end;
  hence thesis;
end;
