
theorem  :: Proposition 6 5L'
  for R being non empty mediate RelStr,
      X being Subset of R holds
    LAp (LAp X) c= LAp X
  proof
    let R be non empty mediate RelStr;
    let X be Subset of R;
A1: LAp (LAp X) = LAp ((LAp X)``)
               .= (UAp (LAp (X``))`)` by Th16
               .= (UAp ((UAp (X`))``))` by Th16
               .= (UAp (UAp (X`)))`;
    (UAp (X`))` = LAp (X``) by Th16
               .= LAp X;
    hence thesis by A1,SUBSET_1:12,Th39;
  end;
