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
  for f1,f2,g1,g2 being Loop of t,
      F being Homotopy of f1,f2, G being Homotopy of g1,g2
  st f1,f2 are_homotopic & g1,g2 are_homotopic holds
  HomotopyMlt(F,G) is Homotopy of LoopMlt(f1,g1),LoopMlt(f2,g2)
  proof
    let f1,f2,g1,g2 be Loop of t,
        F be Homotopy of f1,f2, G be Homotopy of g1,g2 such that
A1: f1,f2 are_homotopic & g1,g2 are_homotopic;
    thus LoopMlt(f1,g1),LoopMlt(f2,g2) are_homotopic by A1,Th9;
    F is continuous & G is continuous by A1,BORSUK_6:def 11;
    hence HomotopyMlt(F,G) is continuous;
    thus thesis by A1,Lm2;
  end;
