reserve T for BinContinuous unital TopSpace-like non empty TopGrStr,
  x,y for Point of I[01],
  s,t for unital Point of T,
  f,g for Loop of t,
  c for constant Loop of t;

theorem Th9:
  for f1,f2,g1,g2 being Loop of t
  st f1,f2 are_homotopic & g1,g2 are_homotopic holds
  LoopMlt(f1,g1),LoopMlt(f2,g2) are_homotopic
  proof
    let f1,f2,g1,g2 be Loop of t;
    assume
A1: f1,f2 are_homotopic;
    then consider F being Function of II,T such that
A2: F is continuous &
    for x being Point of I holds F.(x,0) = f1.x & F.(x,1) = f2.x &
    F.(0,x) = t & F.(1,x) = t;
    assume
A3: g1,g2 are_homotopic;
    then consider G being Function of II,T such that
A4: G is continuous &
    for x being Point of I holds G.(x,0) = g1.x & G.(x,1) = g2.x &
    G.(0,x) = t & G.(1,x) = t;
    take HomotopyMlt(F,G);
    F is Homotopy of f1,f2 & G is Homotopy of g1,g2
    by A2,A4,A1,A3,BORSUK_6:def 11;
    hence thesis by A1,A2,A3,A4,Lm2;
  end;
