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
  x0,x1 are_connected implies pi_1(X,x0), pi_1(X,x1) are_isomorphic
proof
  set P = the Path of x1,x0;
  assume
A1: x0,x1 are_connected;
  then reconsider
  h = pi_1-iso(P) as Homomorphism of pi_1(X,x0), pi_1(X,x1) by Th50;
  take h;
  thus thesis by A1,Th55;
end;
