reserve A for non empty AltCatStr,
  B, C for non empty reflexive AltCatStr,
  F for feasible Covariant FunctorStr over A, B,
  G for feasible Covariant FunctorStr over B, C,
  M for feasible Contravariant FunctorStr over A, B,
  N for feasible Contravariant FunctorStr over B, C,
  o1, o2 for Object of A,
  m for Morphism of o1, o2;
reserve A, B, C, D for transitive with_units non empty AltCatStr,
  F1, F2, F3 for covariant Functor of A, B,
  G1, G2, G3 for covariant Functor of B, C,
  H1, H2 for covariant Functor of C, D,
  p for transformation of F1, F2,
  p1 for transformation of F2, F3,
  q for transformation of G1, G2,
  q1 for transformation of G2, G3,
  r for transformation of H1, H2;

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;
