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 Th72:
  uInt.n = No_Ordinal_op n
proof
  defpred P[Nat] means uInt.$1 = No_Ordinal_op $1;
A1:P[0] by Def1,Th64;
A2:P[m] implies P[m+1]
  proof
    assume
A3: P[m];
    Segm (m+1) = succ Segm m by NAT_1:38;
    hence No_Ordinal_op (m+1) = [{No_Ordinal_op m},{}] by Th65
    .= uInt.(m+1) by Def1,A3;
  end;
  P[m] from NAT_1:sch 2(A1,A2);
  hence thesis;
end;
