reserve A,B for Ordinal,
        o for object,
        x,y,z for Surreal,
        n for Nat,
        r,r1,r2 for Real;

theorem
  x == 0_No iff |.x.| == 0_No
proof
  thus x == 0_No implies |.x.| == 0_No by Def6;
  assume
A1: |.x.| == 0_No;
  thus x <= 0_No by A1,Def6;
  assume x < 0_No;
  then 0_No = -0_No < -x & |.x.| = -x by Def6,SURREALR:10;
  hence thesis by A1;
end;
