reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

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;
