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 Th25:
  p in halfline(p,q)
proof
  (1-0)*p + 0 * q = p + 0 * q by RLVECT_1:def 8
    .= p + 0.V by RLVECT_1:10
    .= p by RLVECT_1:4;
  hence thesis;
end;
