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;
reserve t for natural_transformation of F,F1,
  t1 for natural_transformation of F1,F2;

theorem
  F1 ~= F2 implies F2 ~= F1
proof
  assume
A1: F1 is_naturally_transformable_to F2;
  given t being natural_transformation of F1,F2 such that
A2: t is invertible;
  thus F2 is_naturally_transformable_to F1 by A1,A2,Lm5;
  take t";
  let a be Object of A;
  t".a = (t.a)" by A1,A2,Th23;
  hence thesis by A2,CAT_1:46;
end;
