
theorem Th7:
  for L being non empty RelStr holds L is connected iff L opp is connected
proof
  let L be non empty RelStr;
  thus L is connected implies L opp is connected
  proof
    assume
A1: for x,y being Element of L holds x <= y or x >= y;
    let x,y be Element of L opp;
    ~x <= ~y or ~x >= ~y by A1;
    hence thesis by Th1;
  end;
  assume
A2: for x,y being Element of L opp holds x <= y or x >= y;
  let x,y be Element of L;
  x~ <= y~ or x~ >= y~ by A2;
  hence thesis by LATTICE3:9;
end;
