theorem
  G1 is_transformable_to G2 implies q*F1 = q (#) idt F1
proof
  assume G1 is_transformable_to G2;
  then G1*F1 is_transformable_to G2*F1 by Th10;
  hence q*F1 = (q*F1)`*`(idt(G1*F1)) by FUNCTOR2:5
    .= q (#) idt F1 by Th19;
end;
