reserve A,B,C for Category,
  F,F1 for Functor of A,B;
reserve o,m for set;
reserve t for natural_transformation of F,F1;

theorem Th36:
  for F1,G1 being Functor of A,B, F2,G2 being Functor of A,C st F1
is_naturally_transformable_to G1 & F2 is_naturally_transformable_to G2 holds <:
  F1,F2:> is_naturally_transformable_to <:G1,G2:>
proof
  let F1,G1 be Functor of A,B, F2,G2 be Functor of A,C such that
A1: F1 is_naturally_transformable_to G1 & F2 is_naturally_transformable_to G2;
  F1 is_transformable_to G1 & F2 is_transformable_to G2 by A1;
  hence <:F1,F2:> is_transformable_to <:G1,G2:> by Th34;

set t1 = the natural_transformation of F1,G1,t2 = the natural_transformation of
F2,G2;
  take <:t1,t2:>;
  thus thesis by A1,Lm4;
end;
