
theorem Th4:
  for L being RelStr holds L is reflexive iff L opp is reflexive
proof
  let L be RelStr;
  thus L is reflexive implies L opp is reflexive
  proof
    assume L is reflexive;
    then
A1: the InternalRel of L is_reflexive_in the carrier of L;
    let x be object;
    assume x in the carrier of L opp;
    then [x,x] in the InternalRel of L by A1;
    hence thesis by RELAT_1:def 7;
  end;
  assume L opp is reflexive;
  then
A2: the InternalRel of L opp is_reflexive_in the carrier of L opp;
  let x be object;
  assume x in the carrier of L;
  then [x,x] in the InternalRel of L opp by A2;
  hence thesis by RELAT_1:def 7;
end;
