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 Th35:
  for F1,G1 being Functor of A,B, F2,G2 being Functor of A,C st F1
is_transformable_to G1 & F2 is_transformable_to G2 for t1 being transformation
of F1,G1, t2 being transformation of F2,G2 for a being Object of A holds <:t1,
  t2:>.a = [t1.a,t2.a]
proof
  let F1,G1 be Functor of A,B, F2,G2 be Functor of A,C such that
A1: F1 is_transformable_to G1 & F2 is_transformable_to G2;
  let t1 be transformation of F1,G1, t2 be transformation of F2,G2;
  let a be Object of A;
  reconsider s1 = t1 as Function of the carrier of A, the carrier' of B;
  reconsider s2 = t2 as Function of the carrier of A, the carrier' of C;
  thus <:t1,t2:>.a = (<:t1,t2:> qua Function of the carrier of A, the carrier'
  of [:B,C:]).a by A1,Th34,NATTRA_1:def 5
    .= <:s1,s2:>.a by A1,Def11
    .= [t1.a,t2.a] by A1,Lm2;
end;
