
theorem
  for L being reflexive RelStr holds
  id the carrier of L c= the InternalRel of L
proof
  let L be reflexive RelStr;
  for a,b being object st [a,b] in id the carrier of L holds [a,b] in the
  InternalRel of L
  proof
    let a,b be object;
    assume [a,b] in id the carrier of L;
    then
A1: a = b & a in the carrier of L by RELAT_1:def 10;
    the InternalRel of L is_reflexive_in the carrier of L by ORDERS_2:def 2;
    hence thesis by A1,RELAT_2:def 1;
  end;
  hence thesis by RELAT_1:def 3;
end;
