 reserve f,g for Function;
 reserve R for non empty reflexive RelStr;
 reserve R for non empty RelStr;

theorem :: c)
  for f being map of R holds
    f.{} = {} iff (Flip f).(the carrier of R) = the carrier of R
  proof
    let f be map of R;
    thus f.{} = {} implies (Flip f).(the carrier of R) = the carrier of R
      by ROUGHS_2:18;
    set g = Flip f;
A1: Flip Flip f = f by ROUGHS_2:23;
    thus (Flip f).(the carrier of R) = the carrier of R implies f.{} = {}
      by A1,ROUGHS_2:19;
  end;
