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
  for x being set holds x in halfline(p,q) iff ex l being Real
 st x = (1-l)*p + l*q & 0 <= l;
