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

theorem Th7:
  L_(uInt.-n) = {} = R_(uInt.n)
proof
A1: uInt.0 = 0_No by Def1;
  thus L_(uInt.-n) = {}
  proof
    assume
A2: L_(uInt.-n) <> {};
    then n <>0 by A1;
    then reconsider N=n-1 as Nat by NAT_1:20;
    uInt.-(N+1) = [{},{uInt.-N}] by Def1;
    hence thesis by A2;
  end;
  assume
A3:R_(uInt.n) <> {};
  then n <> 0 by A1;
  then reconsider N=n-1 as Nat by NAT_1:20;
  uInt.(N+1) = [{uInt.N},{}] by Def1;
  hence thesis by A3;
end;
