reserve n for Nat,
  a, b, r, w for Real,
  x, y, z for Point of TOP-REAL n,
  e for Point of Euclid n;
reserve V for RealLinearSpace,
        p,q,x for Element of V;

theorem Th27:
  halfline(p,p) = {p}
proof
  hereby
    let d be object;
    assume d in halfline(p,p);
    then ex r being Real st d = (1-r)*p+r*p & 0 <= r;
    then d = p by Th2;
    hence d in {p} by TARSKI:def 1;
  end;
  let d be object;
  assume d in {p};
  then d = p by TARSKI:def 1;
  hence thesis by Th25;
end;
