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 Th20:
  F1 is_naturally_transformable_to F2 implies for t being
  natural_transformation of F1,F2 holds (id F2)`*`t = t & t`*`(id F1) = t
proof
  assume
A1: F1 is_naturally_transformable_to F2;
  then
A2: F1 is_transformable_to F2;
  let t be natural_transformation of F1,F2;
  thus (id F2)`*`t = (id F2)`*`(t qua transformation of F1,F2) by A1,Def8
    .= t by A2,Th17;
  thus t`*`(id F1) = (t qua transformation of F1,F2)`*`(id F1) by A1,Def8
    .= t by A2,Th17;
end;
