
theorem Th16:
  for C being CategoryStr, a,b being Object of C,
      f being Morphism of a,b st Hom(a,b) <> {}
  holds ex f1,f2 being morphism of C st a = f1 & b = f2 & f |> f1 & f2 |> f
  proof
    let C be CategoryStr;
    let a,b be Object of C;
    let f be Morphism of a,b;
    assume Hom(a,b) <> {};
    then f in Hom(a,b) by Def3;
    then consider f11 be morphism of C such that
A1: f11 = f & ex f1,f2 being morphism of C
    st a = f1 & b = f2 & f11 |> f1 & f2 |> f11;
    thus thesis by A1;
  end;
