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 Th44:
  uDyadic.([/ r*(2|^n)-1\] / (2|^n))
    < sReal.r <
      uDyadic.([\ r*(2|^n)+1/] / (2|^n))
proof
  set R=sReal.r;
  L_R << {R} << R_R & R in {R} by SURREALO:11,TARSKI:def 1;
  hence thesis by Th42,Th43;
end;
