 reserve f,g for Function;
 reserve R for non empty reflexive RelStr;
 reserve R for non empty RelStr;
 reserve f for Function of the carrier of R, bool the carrier of R;

theorem FlipMono:
  for f being map of R st f is c=-monotone holds
    Flip f is c=-monotone
  proof
    let f be map of R;
    set g = Flip f;
    assume
A1: f is c=-monotone;
    for A,B being Subset of R st A c= B holds g.A c= g.B
    proof
      let A,B be Subset of R;
      assume A c= B; then
      B` c= A` by SUBSET_1:12; then
      f.B` c= f.A` by A1; then
      (f.A`)` c= (f.B`)` by SUBSET_1:12; then
      g.A c= (f.B`)` by ROUGHS_2:def 14;
      hence thesis by ROUGHS_2:def 14;
    end;
    hence thesis;
  end;
