 reserve A,B,O for Ordinal,
      n,m for Nat,
      a,b,o for object,
      x,y,z for Surreal,
      X,Y,Z for set,
      Inv,I1,I2 for Function;

theorem
  not x==0_No implies x" " == x
proof
  assume not x==0_No;
  then
A1:0_No < 1_No == x*x" by Th33,Def8;
  then not x*x" == 0_No by SURREALO:4;
  then not x" == 0_No by SURREALR:72,74;
  hence thesis by A1,Th41;
end;
