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

theorem     :: ZFMISC_1:42
  A = EmptyMS I or A = {x1} or A = {x2} or A = {x1,x2} implies A c= {x1,x2}
proof
  assume
A1: A = EmptyMS I or A = {x1} or A = {x2} or A = {x1,x2};
  let i such that
A2: i in I;
  per cases by A1;
  suppose A = EmptyMS I;
    then A.i = {} by PBOOLE:5;
    then A.i c= {x1.i,x2.i} by ZFMISC_1:36;
    hence thesis by A2,Def2;
  end;
  suppose A = {x1};
    then A.i = {x1.i} by A2,Def1;
    then A.i c= {x1.i,x2.i} by ZFMISC_1:36;
    hence thesis by A2,Def2;
  end;
  suppose A = {x2};
    then A.i = {x2.i} by A2,Def1;
    then A.i c= {x1.i,x2.i} by ZFMISC_1:36;
    hence thesis by A2,Def2;
  end;
  suppose A = {x1,x2};
    hence thesis;
  end;
end;
