
theorem LApInt:
  for T being naturally_generated non empty with_equivalence TopRelStr,
      A being Subset of T holds
    LAp A = Int A
  proof
    let T be naturally_generated non empty with_equivalence TopRelStr,
        A be Subset of T;
    Int A c= LAp A
    proof
      let x be object;
      assume
A1:   x in Int A; then
      reconsider xx = x as set;
      consider Q being Subset of T such that
A2:   Q is open & Q c= A & xx in Q by TOPS_1:22,A1;
      Q = Int Q by A2,TOPS_1:23; then
A3:   Q = LAp Q by OpenLap;
      LAp Q c= LAp A by A2,ROUGHS_1:24;
      hence thesis by A2,A3;
    end;
    hence thesis by TOPS_1:24,ROUGHS_1:12;
  end;
