
theorem Th3:
  for C being composable CategoryStr,
      f,f1,f2 being morphism of C st f1 |> f2
  holds
  (f1(*)f2 |> f iff f2 |> f) &
  (f |> f1(*)f2 iff f |> f1)
  proof
    let C be composable CategoryStr;
    let f,f1,f2 be morphism of C;
    assume
A1: f1 |> f2;
    C is left_composable & C is right_composable by CAT_6:def 11;
    hence thesis by A1,CAT_6:def 8,def 9;
  end;
