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 Th28:
  for l being Loop of [s,t] holds FGPrIso(s,t).Class(EqRel([:S,T:]
  ,[s,t]),l) = <*Class(EqRel(S,s),pr1 l),Class(EqRel(T,t),pr2 l)*>
proof
  let l be Loop of [s,t];
  Class(EqRel([:S,T:],[s,t]),l) is Point of pi_1([:S,T:],[s,t]) by TOPALG_1:47;
  hence thesis by Th27;
end;
