
theorem CharIsPref:
  for A being non empty set,
      R being total reflexive Relation of A holds
    CharPrefSpace R is preference-like
  proof
    let A be non empty set,
        R be total reflexive Relation of A;
    set X = CharPrefSpace R;
    set P = X;
XX: the carrier of P = A &
     the PrefRel of P = R /\ (R~)` &
     the ToleranceRel of P = R /\ R~ &
     the InternalRel of P = Aux R by Def55;
    thus thesis by LEM1,XX,SumNabla2,MutuDis2,LEM3b,LEM2a;
  end;
