theorem
  ex r1,r2 being Element of REALPLUS st
  intrval(f1,f2) = REAL_ratio(r1,r2)
  proof
    the carrier of MS c= REALPLUS by Def07a;
    then reconsider r1 = f1,r2 = f2 as Element of REALPLUS;
    consider r,s be positive Real such that
A1: r1 = r & r2 = s & REAL_ratio(r1,r2) = s / r by Def01;
    intrval(f1,f2) = s / r & REAL_ratio(r1,r2) = s / r by A1,Def21;
    hence thesis;
  end;
