
theorem Th19:
  for X being non empty set, Y being non empty Subset of ExtREAL
  for F being Function of X,Y holds inf(- F) = - sup F & sup(- F) = - inf F
proof
  let X be non empty set;
  let Y be non empty Subset of ExtREAL;
  let F be Function of X,Y;
  thus inf(- F) = inf(- rng F) by Th18
    .= - sup F by Th13;
  thus sup(- F) = sup(- rng F) by Th18
    .= - inf F by Th14;
end;
