theorem Th46:
  for f being UnOp of BooleLatt A holds f is monotone iff f is c=-monotone
proof
  let f be UnOp of BooleLatt A;
  thus f is monotone implies f is c=-monotone
  proof
    assume
A1: f is monotone;
    let x, y be Element of BooleLatt A;
    assume x c= y;
    then x [= y by LATTICE3:2;
    then f.x [= f.y by A1;
    hence thesis by LATTICE3:2;
  end;
  assume
A2: f is c=-monotone;
  let p, q be Element of BooleLatt A;
  assume p [= q;
  then p c= q by LATTICE3:2;
  then f.p c= f.q by A2;
  hence f.p [= f.q by LATTICE3:2;
end;
