theorem Th12:
  F absorbs G implies F/\/RD absorbs G/\/RD
proof
  deffunc Cl(Element of D) = EqClass(RD,$1);
  defpred P[Element of Class RD,Element of Class RD] means (F/\/RD).($1,(G/\/
  RD).($1,$2)) = $1;
  assume
A1: for x,y being Element of D holds F.(x,G.(x,y)) = x;
A2: now
    let x1,x2 be Element of D;
    (F/\/RD).(Cl(x1),(G/\/RD).(Cl(x1),Cl(x2))) = (F/\/RD).(Cl(x1),Cl(G.(x1
    ,x2))) by Th3
      .= Cl(F.(x1,G.(x1,x2))) by Th3
      .= Cl(x1) by A1;
    hence P[EqClass(RD,x1),EqClass(RD,x2)];
  end;
  thus for x,y being Element of Class RD holds P[x,y] from SchAux2(A2);
end;
