
theorem Th1:
  for C being composable associative CategoryStr,
      f1,f2,f3 being morphism of C st f1 |> f2 & f2 |> f3 holds
   f1(*)f2(*)f3 = f1(*)(f2(*)f3)
  proof
    let C be composable associative CategoryStr;
    let f1,f2,f3 be morphism of C;
    assume
A1: f1 |> f2 & f2 |> f3;
    C is left_composable right_composable by CAT_6:def 11;
    then f1(*)f2 |> f3 & f1 |> f2(*)f3 by A1,CAT_6:def 8,def 9;
    hence f1(*)f2(*)f3 = f1(*)(f2(*)f3) by A1,CAT_6:def 10;
  end;
