reserve A,B,C,D for Category,
  F for Functor of A,B,
  G for Functor of B,C;
reserve o,m for set;
reserve F,F1,F2,F3 for Functor of A,B,
  G,G1,G2,G3 for Functor of B,C,
  H,H1,H2 for Functor of C,D,
  s for natural_transformation of F1,F2,
  s9 for natural_transformation of F2,F3,
  t for natural_transformation of G1,G2,
  t9 for natural_transformation of G2,G3,
  u for natural_transformation of H1,H2;

theorem
  G1 is_naturally_transformable_to G2 implies t(#)(id id B) = t
proof
  assume
A1: G1 is_naturally_transformable_to G2;
  then
A2: G1*id B is_naturally_transformable_to G2*id B by Th20;
  thus t(#)(id id B) = (t*id B)`*`id(G1*id B) by Th31
    .= t*id B by A2,NATTRA_1:24
    .= t by A1,Th32;
end;
