reserve p, q, x, y for Real,
  n for Nat;
reserve X for non empty TopSpace,
  a, b, c, d, e, f for Point of X,
  T for non empty pathwise_connected TopSpace,
  a1, b1, c1, d1, e1, f1 for Point of T;
reserve x0, x1 for Point of X,
  P, Q for Path of x0,x1,
  y0, y1 for Point of T,
  R, V for Path of y0,y1;

theorem Th59:
  for a, b being Point of TOP-REAL n, P, Q being Path of a,b holds
  P, Q are_homotopic
proof
  let a, b be Point of TOP-REAL n, P, Q be Path of a,b;
  take F = RealHomotopy(P,Q);
  thus F is continuous by Lm5;
  thus thesis by Lm6;
end;
