reserve X,Y,x,y for set;
reserve A for non empty Poset;
reserve a,a1,a2,a3,b,c for Element of A;
reserve S,T for Subset of A;

theorem Th8:
  for A being non empty reflexive RelStr for a being Element of A
  holds {a} is Chain of A
proof
  let A be non empty reflexive RelStr, a be Element of A;
A1: the InternalRel of A is_reflexive_in the carrier of A by Def2;
  {a} is strongly_connected
  proof
    let x1,x2 be object;
    assume x1 in {a} & x2 in {a};
    then x1 = a & x2 = a by TARSKI:def 1;
    hence thesis by A1;
  end;
  hence thesis;
end;
