reserve S, T, Y for non empty TopSpace,
  s, s1, s2, s3 for Point of S,
  t, t1, t2, t3 for Point of T,
  l1, l2 for Path of [s1,t1],[s2,t2],
  H for Homotopy of l1 ,l2;

theorem
  for f being Homomorphism of pi_1(S,s1),pi_1(S,s2), g being
Homomorphism of pi_1(T,t1),pi_1(T,t2) st f is bijective & g is bijective holds
  Gr2Iso(f,g) * FGPrIso(s1,t1) is bijective
proof
  let f be Homomorphism of pi_1(S,s1),pi_1(S,s2), g be Homomorphism of pi_1(T,
  t1),pi_1(T,t2);
  assume f is bijective & g is bijective;
  then
A1: Gr2Iso(f,g) is bijective by Th5;
  FGPrIso(s1,t1) is bijective;
  hence thesis by A1,GROUP_6:64;
end;
