theorem
  for S being Subset of TOP-REAL 2, p,q be Point of TOP-REAL 2 st p <> q
  & LSeg(p,q) \ {p,q} c= S holds LSeg(p,q) c= Cl S
proof
  let S be Subset of TOP-REAL 2, p,q be Point of TOP-REAL 2 such that
A1: p <> q;
  assume LSeg(p,q) \ {p,q} c= S;
  then Cl(LSeg(p,q) \ {p,q}) c= Cl S by PRE_TOPC:19;
  hence thesis by A1,Th2;
end;
