theorem
  F1 is_transformable_to F2 implies G1*p = (idt G1) (#) p
proof
  assume F1 is_transformable_to F2;
  then G1*F1 is_transformable_to G1*F2 by Th10;
  hence G1*p = (idt (G1*F2))`*`(G1*p) by FUNCTOR2:5
    .= (idt G1) (#) p by Th18;
end;
