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;
reserve p, q, x for Point of TOP-REAL n;
reserve s, t for Point of TOP-REAL 2;

theorem Th62:
 for V being RealLinearSpace, p1,p2 being Point of V
  holds halfline(p1,p2) c= Line(p1,p2)
proof
 let V be RealLinearSpace, p1,p2 be Point of V;
 let e be object;
 assume e in halfline(p1,p2);
  then ex r st e =(1-r)*p1 + r*p2 & 0 <= r;
 hence e in Line(p1,p2);
end;
