reserve T,U for non empty TopSpace;
reserve t for Point of T;
reserve n for Nat;

theorem Th11:
  T is having_trivial_Fundamental_Group implies
  for t being Point of T, P,Q being Loop of t holds
  P,Q are_homotopic
  proof
    assume
A1: T is having_trivial_Fundamental_Group;
    let t be Point of T, P,Q be Loop of t;
    set E = EqRel(T,t);
A2: pi_1(T,t) is trivial by A1;
    Class(E,P) in the carrier of pi_1(T,t) &
    Class(E,Q) in the carrier of pi_1(T,t) by TOPALG_1:47;
    then Class(E,P) = Class(E,Q) by A2;
    hence thesis by TOPALG_1:46;
  end;
