
theorem Th8:
  for C being non empty composable with_identities CategoryStr,
      f1,f2 being morphism of C st dom f1 = f2 holds f1 |> f2 & f1 (*) f2 = f1
  proof
    let C be non empty composable with_identities CategoryStr;
    let f1,f2 be morphism of C;
    assume dom f1 = f2;
    then consider f be morphism of C such that
A1: f2 = f & f1 |> f & f is identity by CAT_6:def 18;
    thus f1 |> f2 by A1;
    thus f1 (*) f2 = f1 by A1,CAT_6:def 5,def 14;
  end;
