
theorem  :: Proposition 5 3L
  for R being non empty reflexive RelStr,
      X being Subset of R holds
    LAp X c= X
  proof
    let R be non empty reflexive RelStr;
    let X be Subset of R;
    let y be object;
    assume y in LAp X; then
    consider z being Element of R such that
A1: z = y & Class (the InternalRel of R,z) c= X;
A2: z in field the InternalRel of R by Th1;
A3: z in {z} by TARSKI:def 1;
    [z,z] in the InternalRel of R by A2,RELAT_2:def 1,def 9; then
    z in (the InternalRel of R) .: {z} by RELAT_1:def 13,A3;
    hence thesis by A1;
  end;
