reserve A,B,C for Category,
  F,F1,F2,F3 for Functor of A,B,
  G for Functor of B, C;
reserve m,o for set;

theorem Th14:
  F is_transformable_to F1 & F1 is_transformable_to F2 implies F
  is_transformable_to F2
proof
  assume that
A1: F is_transformable_to F1 and
A2: F1 is_transformable_to F2;
  let a be Object of A;
A3: Hom(F1.a,F2.a) <> {} by A2;
  Hom(F.a,F1.a) <> {} by A1;
  hence thesis by A3,CAT_1:24;
end;
