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

theorem
  for T being non empty interval SubSpace of R^1, a, b be Point of T, P, Q
  be Path of a,b holds R1Homotopy(P,Q) is Homotopy of P,Q
proof
  let T be non empty interval SubSpace of R^1, a, b be Point of T, P, Q be Path
  of a,b;
  thus P, Q are_homotopic by Th12;
  thus R1Homotopy(P,Q) is continuous;
  thus thesis by Lm9;
end;
