 reserve n,m for Nat,
      o for object,
      p for pair object,
      x,y,z for Surreal;

theorem Th11:
  for X1,X2,Y1,Y2 be set st X1 c= X2 & Y1 c= Y2 holds
    sqrt(o,X1,Y1) c= sqrt(o,X2,Y2)
proof
  let X1,X2,Y1,Y2 be set such that A1:X1 c= X2 & Y1 c= Y2;
  let a be object;
  assume a in sqrt(o,X1,Y1);
  then ex x1,y1 be Surreal st x1 in X1 & y1 in Y1 & not x1 + y1 == 0_No &
  a = (o +'(x1 * y1)) * (x1+y1)" by Def2;
  hence thesis by A1,Def2;
end;
