theorem
  for a, b be Point of TOP-REAL n, P, Q be Path of a,b holds
  RealHomotopy(P,Q) is Homotopy of P,Q
proof
  let a, b be Point of TOP-REAL n, P, Q be Path of a,b;
  thus P, Q are_homotopic by Th59;
  thus RealHomotopy(P,Q) is continuous;
  thus thesis by Lm6;
end;
