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 Th11:
  for o being Object of A st F1 is_transformable_to F2 holds (G1*p
  )!o = G1.(p!o)
proof
  let o be Object of A;
  assume
A1: F1 is_transformable_to F2;
  then G1*F1 is_transformable_to G1*F2 by Th10;
  hence (G1*p)!o = (G1*p).o by FUNCTOR2:def 4
    .= G1.(p!o) by A1,Def1;
end;
