reserve A,B,C,O for Ordinal,
        X for set,
        o for object,
        x,y,z,t,r,l for Surreal;
reserve n for Nat;

theorem  Th39:
  O c= A c= B implies (unique_No_op A).O = (unique_No_op B).O
proof
  assume A1:O c= A c= B;
  O in succ A by A1,ORDINAL1:6,12;
  then ((unique_No_op B)| succ A).O = (unique_No_op B).O by FUNCT_1:49;
  hence thesis by A1,Th37;
end;
