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 Th70:
  born No_Ordinal_op A = A
  proof
A1: No_Ordinal_op A in Day A by Th67;
    for O st No_Ordinal_op A in Day O holds A c= O
    proof
      let O such that
A2:   No_Ordinal_op A in Day O & not A c= O;
      No_Ordinal_op O < No_Ordinal_op A by Th68,A2,ORDINAL1:16;
      hence thesis by Th69,A2;
    end;
    hence thesis by A1,SURREAL0:def 18;
  end;
