theorem Th13:
  for A being Subset of TOP-REAL n, B being Subset of TOP-REAL n
  st B is_inside_component_of A holds B c= BDD A
proof
  let A be Subset of TOP-REAL n, B be Subset of TOP-REAL n;
  assume B is_inside_component_of A;
  then
A1: B in {B2 where B2 is Subset of TOP-REAL n: B2 is_inside_component_of A};
  let x be object;
  assume x in B;
  hence thesis by A1,TARSKI:def 4;
end;
