reserve A,B,O for Ordinal,
        o for object,
        x,y,z for Surreal,
        n,m for Nat;
reserve d,d1,d2 for Dyadic;
reserve i,j for Integer,
        n,m,p for Nat;
reserve r,r1,r2 for Real;

theorem
  x is No_ordinal implies ex A st x == No_uOrdinal_op A
proof
  assume x is No_ordinal;
  then consider A such that
A1:x == No_Ordinal_op A by Lm24;
  No_Ordinal_op A == No_uOrdinal_op A by Th73;
  then x == No_uOrdinal_op A by A1,SURREALO:4;
  hence thesis;
end;
