reserve n for Element of NAT,
  a, b for Real;

theorem
  for n being Element of NAT, T being non empty convex SubSpace of
TOP-REAL n, a, b being Point of T, P, Q being Path of a,b holds ConvexHomotopy(
  P,Q) is Homotopy of P,Q
proof
  let n be Element of NAT, T be non empty convex SubSpace of TOP-REAL n, a, b
  be Point of T, P, Q be Path of a,b;
  thus P, Q are_homotopic by Th2;
  thus ConvexHomotopy(P,Q) is continuous;
  thus thesis by Lm6;
end;
