reserve A,B,O for Ordinal,
        o for object,
        x,y,z for Surreal,
        n,m for Nat;

theorem Th9:
  for i,j be Integer holds i < j iff uInt.i < uInt.j
proof
  let i,j be Integer;
  thus i < j implies uInt.i < uInt.j by Lm4;
  assume
A1:uInt.i < uInt.j & j <=i;
  then j <> i by SURREALO:3;
  then j < i by A1,XXREAL_0:1;
  then uInt.j <= uInt.i by Lm4;
  hence thesis by A1;
end;
