
theorem Th19:
  {p where p is Point of TOP-REAL 2 : p`2 >= 1 - 2 * p`1 & p`2 >=
  2 * p`1 - 1 } is closed Subset of TOP-REAL 2
proof
  defpred R[Point of TOP-REAL 2] means $1`2 >= 2 * $1`1 - 1;
  reconsider L = { p where p is Point of TOP-REAL 2 : R[p] } as closed Subset
  of TOP-REAL 2 by Th16;
  defpred P[Point of TOP-REAL 2] means $1`2 >= 1 - 2 * $1`1;
  reconsider K = { p where p is Point of TOP-REAL 2 : P[p] } as closed Subset
  of TOP-REAL 2 by Th18;
  set T = {p where p is Point of TOP-REAL 2 : P[p] & R[p] };
  {p where p is Point of TOP-REAL 2 : P[p] & R[p] } = { p where p is Point
  of TOP-REAL 2 : P[p] } /\ { p where p is Point of TOP-REAL 2 : R[p] } from
  DOMAIN_1:sch 10;
  then T = K /\ L;
  hence thesis;
end;
